1) Problem #PRAJXYX "PRAJXYX - TI - 83 Linear Regression - ASSIGN First." |
A)
Visit the STATS4STEM help page on using the TI-83/84 for linear regression. Work through the example provided on the previous link to help you complete the remaining questions. Click "completed" below when you have finished the example. © STATS4STEM.ORG |
Multiple Choice:
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B)
Using your TI-83 and the data shown below, determine the slope of the least-squares regression line that models the linear relationship between x and y. Assume that x is the explanatory or predictor variable and y is the response variable. Round answer to the nearest hundredths. |
Algebraic Expression:
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C)
Using your TI-83, determine the y-intercept of the least-squares regression line. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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D)
Using your TI-83, determine the correlation between x and y. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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E)
Which of the graphs below best represents the correct scatterplot with fitted linear regression line? |
Multiple Choice:
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F)
Which of the graphs below best represents the correct residual plot for the fitted linear regression line? |
Multiple Choice:
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2) Problem #PRAJXZG "PRAJXZG - 258234 - TI - 83 Linear Regression " |
A)
Using your TI-83 and the data shown below, determine the slope of the least-squares regression line that models the linear relationship between x and y. Assume that x is the explanatory or predictor variable and y is the response variable. Round answer to the nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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B)
Using your TI-83, determine the y-intercept of the least-squares regression line. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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C)
Using your TI-83, determine the correlation between x and y. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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D)
Which of the graphs below best represents the correct scatterplot with fitted linear regression line? |
Multiple Choice:
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E)
Which of the graphs below best represents the correct residual plot for the fitted linear regression line? |
Multiple Choice:
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3) Problem #PRAJXZF "PRAJXZF - 258234 - TI - 83 Linear Regression " |
A)
Using your TI-83/84 and the data shown below, determine the slope of the least-squares regression line that models the linear relationship between x and y. Assume that x is the explanatory or predictor variable and y is the response variable. Round answer to the nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
Using your TI-83, determine the y-intercept of the least-squares regression line. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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C)
Using your TI-83, determine the correlation between x and y. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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D)
Which of the graphs below best represents the correct scatterplot with fitted linear regression line? |
Multiple Choice:
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E)
Which of the graphs below best represents the correct residual plot for the fitted linear regression line? |
Multiple Choice:
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4) Problem #PRAJXZE "PRAJXZE - 258234 - TI - 83 Linear Regression " |
A)
Using your TI-83/84 and the data shown below, determine the slope of the least-squares regression line that models the linear relationship between x and y. Assume that x is the explanatory or predictor variable and y is the response variable. Round answer to the nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
Using your TI-83, determine the y-intercept of the least-squares regression line. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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C)
Using your TI-83, determine the correlation between x and y. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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D)
Which of the graphs below best represents the correct scatterplot with fitted linear regression line? |
Multiple Choice:
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E)
Which of the graphs below best represents the correct residual plot for the fitted linear regression line? |
Multiple Choice:
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5) Problem #PRAJYHB "PRAJYHB - 258234 - TI - 83 Linear Regression " |
A)
Using your TI-83/84 and the data shown below, determine the slope of the least-squares regression line that models the linear relationship between x and y. Assume that x is the explanatory or predictor variable and y is the response variable. Round answer to the nearest hundredths. © STATS4STEM.ORG |
Number:
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Hints: |
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B)
Using your TI-83, determine the y-intercept of the least-squares regression line. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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C)
Using your TI-83, determine the correlation between x and y. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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D)
Which of the graphs below best represents the correct scatterplot with fitted linear regression line? |
Multiple Choice:
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E)
Which of the graphs below best represents the correct residual plot for the fitted linear regression line? |
Multiple Choice:
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F)
Calculate the first residual when x=11. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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y-hat = 16.37 - 1.08x Therefore, y-hat = 4.49 |
Residual = 3 - 4.49 = -1.49 (ROUNDED) |
G)
Calculate the residual when x=8. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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y-hat = 16.37 - 1.08x Therefore, y-hat = 7.73 |
Residual = 17 - 7.73 = 9.27 (ROUNDED) |
H)
If you were to calculate all the residuals, what would be the mean of all the residuals? |
Algebraic Expression:
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Hints: |
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I)
What percentage of the variation in y values is explained by using the linear regression model with x as the explanatory variable? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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Answer = 66.80 |
6) Problem #PRAJYHE "PRAJYHE - 258234 - TI - 83 Linear Regression " |
A)
Using your TI-83/84 and the data shown below, determine the slope of the least-squares regression line that models the linear relationship between x and y. Assume that x is the explanatory or predictor variable and y is the response variable. Round answer to the nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
Using your TI-83, determine the y-intercept of the least-squares regression line. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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C)
Using your TI-83, determine the number that represents the stength and direction of the linear association. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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D)
Which of the graphs below best represents the correct scatterplot with fitted linear regression line? |
Multiple Choice:
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E)
Which of the graphs below best represents the correct residual plot for the fitted linear regression line? |
Multiple Choice:
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F)
What number represents the percentage of the variation in y that is explained by using the linear regression model with the x variable as the explanatory variable. *** GIVE PERCENTAGE AS A WHOLE NUMBER *** |
Algebraic Expression:
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Hints: |
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Therefore, Answer = 46 |
7) Problem #PRAJYHD "PRAJYHD - 258234 - TI - 83 Linear Regression " |
A)
Using your TI-83/84 and the data shown below, determine the slope of the least-squares regression line that models the linear relationship between x and y. Assume that x is the explanatory or predictor variable and y is the response variable. Round answer to the nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
Using your TI-83, determine the y-intercept of the least-squares regression line. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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C)
Using your TI-83, determine the correlation between x and y. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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D)
Which of the graphs below best represents the correct scatterplot with fitted linear regression line? |
Multiple Choice:
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E)
Which of the graphs below best represents the correct residual plot for the fitted linear regression line? |
Multiple Choice:
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8) Problem #PRAJYHF "PRAJYHF - 258234 - TI - 83 Linear Regression " |
A)
Using your TI-83 and the data shown below, determine the slope of the least-squares regression line that models the linear relationship between x and y. Assume that x is the explanatory or predictor variable and y is the response variable. Round answer to the nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
Using your TI-83, determine the y-intercept of the least-squares regression line. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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C)
Using your TI-83, determine the correlation between x and y. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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D)
Which of the graphs below best represents the correct scatterplot with fitted linear regression line? |
Multiple Choice:
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E)
Which of the graphs below best represents the correct residual plot for the fitted linear regression line? |
Multiple Choice:
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9) Problem #PRAJ63X "PRAJ63X - 265039 - If correlation is..." |
If correlation is close to zero, we can assume that there is no relationship between the two variables. TRUE or FALSE? © STATS4STEM.ORG |
Multiple Choice:
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10) Problem #PRAJ5ZN "PRAJ5ZN - 264007 - Problem #264007" |
A)
Calculate the slope of the least squares regression line that has the statistics found below. Round answer to the nearest hundredth.
For help, click here for the AP Statistics formula sheet. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
Calculate the y-intercept of the least squares regression line that has the statistics found below. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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b0 = -2.4 - (-0.64)(3.2) |
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C)
Calculate y-hat when x=1. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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When x=1, y-hat = -0.99 |
D)
If y = 0, when x = 1. Calculate the residual. |
Algebraic Expression:
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Hints: |
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E)
Calculate y-hat when x=4. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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When x=4, y-hat = -2.91 (ROUNDED) |
F)
If y = -2, when x = 4. Calculate the residual. |
Algebraic Expression:
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Hints: |
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G)
The direction of this linear regression line is: |
Multiple Choice:
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11) Problem #PRAJXH4 "PRAJXH4 - 257790 - This problem pert..." |
A)
This problem pertains to the forensic glass fragments (fgi) dataset that holds data pertaining to characteristics of glass fragments collected in forensic work. For this problem, we will model glass refractive index (RI) against the percentage by weight of Calcium oxide (Ca). Using the information found above, what is the slope of the least-squares regression line? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
Using the information found above, what is the y-intercept of the least-squares regression line? |
Algebraic Expression:
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Hints: |
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C)
The equation of the regression line is: |
Multiple Choice:
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D)
Interpret the slope of your regression equation in the context of this problem. |
Ungraded Open Response: |
E)
The first six rows of the dataset are found below. Predict RI when Ca is 8.22. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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F)
What is the residual when Ca is 8.22? |
Algebraic Expression:
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Hints: |
OR residual = observed value - predicted value |
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G)
For this problem, the degrees of freedom = 212. How many rows are in our dataset? |
Algebraic Expression:
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Hints: |
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Answer = 214 |
H)
What is S for this problem? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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I)
Below, you will find the scatterplot with fitted regression line and residual plot. Is a linear model appropriate for modeling these data? |
Multiple Choice:
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12) Problem #PRAJV42 "PRAJV42 - 256424 - For the following..." |
A)
For the following data, using your TI-83 or R/Rweb, calculate the slope of the regression line for these two variables. Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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B)
What is the y-intercept? |
Algebraic Expression:
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C)
What is the degrees of freedom? |
Algebraic Expression:
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Hints: |
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13) Problem #PRAJH5B "PRAJH5B - 245862 - This problem pert..." |
A)
This problem pertains to data pertaining to car characteristics. For this problem, we will model MPG.city against Min.Price. Variable Descriptions: Using the information found above, what is the slope of the least-squares regression line? © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
Using the information found above, what is the y-intercept of the least-squares regression line? |
Algebraic Expression:
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Hints: |
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C)
The equation of the regression line is: |
Multiple Choice:
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D)
Interpret the slope of your regression equation in the context of this problem. |
Ungraded Open Response: |
E)
The first row of the dataset is found below. Using your answers to parts A and B, predict the MPG.city when Min.Price is 14.2. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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F)
The first row of the dataset is found below. What is the residual when Min.Price is 14.2? |
Algebraic Expression:
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Hints: |
OR residual = observed value - predicted value |
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G)
For this problem, the degrees of freedom = 46. How many rows are in our dataset? Hint: For linear regression, df = n-2 |
Algebraic Expression:
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Hints: |
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Answer = 48 |
H)
What is S for this problem? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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I)
Below, you will find the scatterplot with fitted regression line and residual plot. Is a linear model appropriate for modeling these data? |
Multiple Choice:
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14) Problem #PRAJH7J "PRAJH7J - 245931 - What is true abou..." |
What is true about the Least-Squares Regression Line? © STATS4STEM.ORG |
Multiple Choice:
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15) Problem #PRAJH7K "PRAJH7K - 245932 - If the correlatio..." |
If the correlation of a set of data is 0, what does this tell you about the data? © STATS4STEM.ORG |
Multiple Choice:
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16) Problem #PRAJH7M "PRAJH7M - 245933 - Correlation" |
Correlation is resistant or not resistant to a few outlying observations? © STATS4STEM.ORG |
Multiple Choice:
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17) Problem #PRAJH7N "PRAJH7N - 245934 - Correlation measu..." |
Correlation measures: © STATS4STEM.ORG |
Multiple Choice:
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18) Problem #PRAJH7V "PRAJH7V - 245941 - What is the defin..." |
A)
What is the definition of 'residual'? © STATS4STEM.ORG |
Multiple Choice:
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B)
What does it mean if the residual for a given point in a set of data is -.2? © STATS4STEM.ORG |
Multiple Choice:
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19) Problem #PRAJH7Y "PRAJH7Y - 245944 - Katy is doing a s..." |
Katy is doing a survey for Perry Pet Grooming. She wants to know if there is a linear relationship between cat age and weight. She collects data from ten cat owners. Age Weight (in lb) 3 8 3 10 5 10 6 11 7 11.25 8 12 9 11.5 12 13 15 16.5 15 20 Find the least-squared regression line for this data. |
Multiple Choice:
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Hints: |
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20) Problem #PRAJ9EQ "PRAJ9EQ - 267295 - Using the compute..." |
A)
Using the computer output below, fill in the value for A. Round answer to the nearest hundredth. © STATS4STEM.ORG |
Number:
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Hints: |
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SEb = b/t |
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B)
The p-value that is represented by the red B, shown in the computer output above, is calculated for which hypothesis test? A) B) C) |
Multiple Choice:
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C)
Refer to the computer output above, what is the value of the red B? Round answer to the nearest hundredths. |
Number:
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Hints: |
This equals 0.2753. However, this a two-sided test. Therefore, we need to multiply this value by 2. Therefore, the p-value = 2*0.2753 = 0.5506 or 0.55 (ROUNDED) Answer = 0.55 |
21) Problem #PRAJ9EW "PRAJ9EW - 267301 - A simulation was ..." |
A)
A simulation was run that created 1000 linear regression lines drawn using 1000 random samples of size 10 drawn from a population of interest. The results of the analysis can be seen in the graphics below: Write a short synopsis of what you believe the three graphs represent. Make sure to note the difference between the 1 black line and the numerous red lines. In addition, how do you think the 2nd and 3rd graphs are related to the first? Make sure to use the following words in your answer: sample, population, alpha, beta © STATS4STEM.ORG |
Ungraded Open Response: |
Hints: |
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B)
From the graphics, one can tell that: |
Multiple Choice:
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C)
It is clear from the second and third graphs that a and b are ___________________ estimators of alpha and beta. |
Exact Match (ignore case):
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Hints: |
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22) Problem #PRAJ9JN "PRAJ9JN - 267417 - Using the compute..." |
A)
Using the computer output below, calculate A. Round answer to the nearest hundredth. © STATS4STEM.ORG |
Number:
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Hints: |
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B)
What is the sample size for this problem? Hint: The degrees of freedom is provided in the output. |
Number:
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Hints: |
df = n - 2 |
Therefore, n = 98 + 2 = 100 |
C)
What is the mean of the residuals for this problem? |
Number:
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Hints: |
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D)
What is the p-value for the hypothesis test below? Round answer to the nearest hundredth. |
Number:
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Hints: |
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23) Problem #PRAJ92E "PRAJ92E - 267875 - In this problem w..." |
A)
In this problem we wish to model the relationship between age and percentage of body fat. The data comes from the agefat dataset that provides the results of a study investigating a new methods of measuring body composition (see Mazess et al, 1984), and give the body fat percentage (percent fat), age and sex for 25 normal adults aged between 23 and 61 years. The questions of interest are how are age and percent fat related. A summary of the linear regression output is provided below: What is the explanatory variable in this analysis? © STATS4STEM.ORG |
Multiple Choice:
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B)
What is the sample size for this dataset? |
Algebraic Expression:
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Hints: |
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For linear regression, df = n - 2 |
n = 23 + 2 = 25 |
C)
What is the number of the point estimate that represent the average increase in the percenatage of body fat for every incease in age of 1 year? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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D)
For inference pertaining to linear regression, the following four conditions must be checked before drawing any valid conclusions. A) True linear relationship between explanatory and response variables. B) Constant variance of residuals. C) Independent observations. D) Residuals are normally distributed. Using the graphics provided below, which of the above conditions appear to be met? Check ALL that appy. |
Check All That Apply:
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E)
You wish to conduct the following hypothesis test for beta: For such a test, what formula would you use to calculate the test statistic? A) B) C) D) E) None of the above |
Multiple Choice:
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F)
What is the SEb? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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G)
Calculate the test statistic for this test. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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H)
If t is 4.2, we can say that the p-value must be: Link to t-table |
Multiple Choice:
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Hints: |
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I)
Is the following statement correct? The p-value we calculated is less than 0.0005. Therefore, we reject the null hypothesis. The data fails to support the claim that the beta, the true slope of the least squares regression line, is greater than 0. Hint - Read question carefully. |
Multiple Choice:
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24) Problem #PRAJ9EP "PRAJ9EP - 267294 - Using the compute..." |
A)
Using the computer output below, fill in the value for A. Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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SEb = b/t |
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B)
Calculate the value of B. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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p-value = tcdf(0.599, 10000, 98) * 2 = 0.55 (ROUNDED) Note: p-value represents two-sided test, therefore, we multiply by 2. |
C)
Calculate the p-value for the following null and alternative hypothesis test: |
Algebraic Expression:
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Hints: |
Alternative Solution: Just divide the p-value calculated in the previous part by 2. |
D)
Calculate the lower limit of a 95% confidence interval for β, the true slope of the least squares regression line. Round only at the END of the problem. Round final answer to the closest hundredth. |
Algebraic Expression:
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Hints: |
0.0621 - (1.990)*(0.1036) = - 0.144 or -0.14 (ROUNDED) |
E)
Fill in the following blank to make the statement below a proper interpretation of the calculated confidence interval. Based on my analysis, I can be 95% ____________________ that β, the true slope of the least squares regression line, falls between -0.14 and 0.27. |
Exact Match (case sensitive):
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Hints: |
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25) Problem #PRAJ9XA "PRAJ9XA - 267778 - Using the compute..." |
A)
Using the computer output for linear regression found below, what percentage of variability in y can be explained by the linear model where x is the explanatory variable? Round percentage to the nearest whole number. © STATS4STEM.ORG |
Exact Match (ignore case):
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Hints: |
r2 = 1.27 or 1 (ROUNDED) |
B)
For linear regression, degrees of freedom equals: |
Multiple Choice:
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C)
Calculate the margin of error needed to construct a 99% confidence interval for the true slope of the least-squares regression line. Round answer to the nearest hundredth. Link to t-table. |
Algebraic Expression:
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Hints: |
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26) Problem #PRAKFE9 "PRAKFE9 - 273078 - Which of the foll..." |
Which of the following are resistant? Check all that apply. © STATS4STEM.ORG |
Check All That Apply:
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Hints: |
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Select 'C' and 'F'. |
27) Problem #PRAKFFQ "PRAKFFQ - 273092 - The blue ..." |
A)
The blue dot in Plot B can be considered a(n): © STATS4STEM.ORG |
Multiple Choice:
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B)
The blue dot in Plot B can be considered a(n): |
Multiple Choice:
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28) Problem #PRARBR4 "PRARBR4 - Problem #418494" |
Based on the two residual plots below, which statement is most correct? |
Multiple Choice:
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29) Problem #PRARBT7 "PRARBT7 - 267417 - Using the compute..." |
A)
Using the computer output below, calculate A. Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
Click here for STATS4STEM help page 1. Click here for STATS4STEM help page 2. |
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B)
What is the sample size for this problem? Hint: The degrees of freedom is provided in the output. |
Algebraic Expression:
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Hints: |
df = n - 2 |
Therefore, n = 38 + 2 = 40 |
C)
What is s for this problem? |
Algebraic Expression:
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Hints: |
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D)
What is the p-value for the hypothesis test below? Round answer to the nearest hundredth. |
Multiple Choice:
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Hints: |
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30) Problem #PRARC6E "PRARC6E - Problem #419837" |
The two plots above were created using data from the gilgais dataset. This dataset was collected on a line transect survey in gilgai territory in New South Wales, Australia. Gilgais are natural gentle depressions in otherwise flat land, and sometimes seem to be regularly distributed. The data collection was stimulated by the question: are these patterns reflected in soil properties? At each of 365 sampling locations on a linear grid, electrical conductivity and chloride content were measured at a spacing of 4 meters. Samples were taken at depths 0-10 cm, 30-40 cm and 80-90 cm. The plots above were created by modeling the choloride content at 30-40 cm against the electrical conductivity at the same depth. By inspecting the two plots, it is clear that: © STATS4STEM.ORG |
Multiple Choice:
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