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> summary(time.lm) Call: lm(formula = Time ~ Ascent, data = HighPeaks) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.2100541 1.8661683 2.256 0.02909 * Ascent 0.0020805 0.0005909 3.521 0.00101 ** What is the fitted regression model? |

2. | Forty-six mountains in the Adirondacks of upstate New York are known as the High Peaks with elevations near or above 4000 feet. Below is some R output from a linear regression model of > summary(time.lm) Call: lm(formula = Time ~ Ascent, data = HighPeaks) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.2100541 1.8661683 2.256 0.02909 * Ascent 0.0020805 0.0005909 3.521 0.00101 ** Interpret the slope of the model in context. |

3. F P t U e | orty-six mountains in the Adirondacks of upstate New York are known as the High eaks with elevations near or above 4000 feet. We regress sing this model, predict the hiking time for a mountain with an ascent of 3000 feet and xplain how much faith you have in that prediction. |

A | ) 6.3 hours |

B | ) Somewhere between 7 and 12 hours, but we can't be more specific |

C | ) 10.5 hours |

D | ) 3004.2 hours |

4. F P t U e | orty-six mountains in the Adirondacks of upstate New York are known as the High eaks with elevations near or above 4000 feet. We regress sing this model, predict the hiking time for a mountain with an ascent of 300 feet and xplain how much faith you have in that prediction. |

A | ) 0.63 hours |

B | ) Somewhere between 0 and 18 hours, but we can't be more specific |

C | ) 4.8 hours |

D | ) 304.2 hours |

5. Forty-six mountains in the Adirondacks of upstate New York are known as the High Peaks with elevations near or above 4000 feet. Below is some R output from a linear regression model of *Y *= *Time *(expected trip time to hike the peak, in hours) on *X *= *Ascent *(in feet).

> summary(time.lm) Call:

lm(formula = Time ~ Ascent, data = HighPeaks)

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) Ascent

4.2100541 1.8661683 2.256 0.02909 *

0.0020805 0.0005909 3.521 0.00101 **

Residual Multiple

standard error: 2.496 on 44 degrees of freedom

R-squared: 0.2198, Adjusted R-squared: 0.2021

F-statistic: 12.4 on 1 and 44 DF, p-value: 0.001014

Report the standard error of regression.

A) 1.86617

B) 0.00059

C) 2.496

D) Values between –4.327 and 6.529

6. | Forty-six mountains in the Adirondacks of upstate New York are known as the High Peaks with elevations near or above 4000 feet. A linear regression model of (expected trip time to hike the peak, in hours) on |

7. | Forty-six mountains in the Adirondacks of upstate New York are known as the High Peaks with elevations near or above 4000 feet. A linear regression model of |

8. | Forty-six mountains in the Adirondacks of upstate New York are known as the High Peaks with elevations near or above 4000 feet. A linear regression model of |

9. | Forty-six mountains in the Adirondacks of upstate New York are known as the High Peaks with elevations near or above 4000 feet. A linear regression model of |

10. | Forty-six mountains in the Adirondacks of upstate New York are known as the High Peaks with elevations near or above 4000 feet. A linear regression model of |

11. F P o (i a n fi B | orty-six mountains in the Adirondacks of upstate New York are known as the High eaks with elevations near or above 4000 feet. The variables include umerical variables in the data set. For instance, the graph in the second column of the rst row shows a scatterplot with ased on these plots, which variable is the best single predictor of |

A | ) |

B | ) |

C | ) |

12. | Cholesterol levels are measured on a sample of 21 volunteers. HDL (high-density lipoprotein, or “good” cholesterol) is regressed on total cholesterol ( > summary(chol.lm) Call: lm(formula = HDL ~ Chol, data = HDL) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 24.32224 8.35551 2.911 0.00896 ** Chol 0.11599 0.03436 3.376 0.00317 ** |

13. | Cholesterol levels are measured on a sample of 21 volunteers. HDL (high-density lipoprotein, or “good” cholesterol) is regressed on total cholesterol ( > summary(chol.lm) Call: lm(formula = HDL ~ Chol, data = HDL) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 24.32224 8.35551 2.911 0.00896 ** Chol 0.11599 0.03436 3.376 0.00317 ** |

14. | Cholesterol levels are measured on a sample of 21 volunteers. HDL (high-density lipoprotein, or “good” cholesterol) is regressed on total cholesterol ( Does it make sense to interpret the intercept of this model? |

15. C li m w | holesterol levels are measured on a sample of 21 volunteers. HDL (high-density poprotein, or “good” cholesterol) is regressed on total cholesterol ( A new patient shows a total cholesterol level of 280 mg/dl. Using this model, what ould you predict as the HDL value for this patient? |

A | ) 32.5 mg/dl |

B | ) 56.8 mg/dl |

C | ) 57.2 mg/dl |

D | ) 304.3 mg/dl |

16. | Cholesterol levels are measured on a sample of 21 volunteers. HDL (high-density lipoprotein, or “good” cholesterol) is regressed on total cholesterol ( |

17. | Cholesterol levels are measured on a sample of 21 volunteers. HDL (high-density lipoprotein, or “good” cholesterol) is regressed on total cholesterol ( |

18. | Cholesterol levels are measured on a sample of 21 volunteers. HDL (high-density lipoprotein, or “good” cholesterol) is regressed on total cholesterol ( |

19. | Cholesterol levels are measured on a sample of 21 volunteers. HDL (high-density lipoprotein, or “good” cholesterol) is regressed on total cholesterol ( |

20. t
| A residuals vs. fitted value plot for a regression model is shown below. Based only on he information in this plot, do you feel the condition of linearity is |

A | ) Reasonable |

B | ) Problematic |

C | ) Can't judge |

21. t
| A residuals vs. fitted value plot for a regression model is shown below. Based only on he information in this plot, do you feel the condition of equal variance is |

A | ) Reasonable |

B | ) Problematic |

C | ) Can't judge |

22. t
| A residuals vs. fitted value plot for a regression model is shown below. Based only on he information in this plot, do you feel the condition of normality is |

A | ) Reasonable |

B | ) Problematic |

C | ) Can't judge |

23. t
| A residuals vs. fitted value plot for a regression model is shown below. Based only on he information in this plot, do you feel the condition of independence is |

A | ) Reasonable |

B | ) Problematic |

C | ) Can't judge |

24. i
| A normal quantile plot for a regression model is shown below. Based only on the nformation in this plot, do you feel the condition of linearity is |

A | ) Reasonable |

B | ) Problematic |

C | ) Can't judge |

25. i
| A normal quantile plot for a regression model is shown below. Based only on the nformation in this plot, do you feel the condition of equal variance is |

A | ) Reasonable |

B | ) Problematic |

C | ) Can't judge |

26. i
| A normal quantile plot for a regression model is shown below. Based only on the nformation in this plot, do you feel the condition of normality is |

A | ) Reasonable |

B | ) Problematic |

C | ) Can't judge |

27. i
| A normal quantile plot for a regression model is shown below. Based only on the nformation in this plot, do you feel the condition of independence is |

A | ) Reasonable |

B | ) Problematic |

C | ) Can't judge |

28. | Below is a scatterplot. You will be adding two points to the graph. Specifically, you will add (1) a point that is an outlier but not influential, which you will draw as an “O,” and (2) a point that is influential but not an outlier, which you will draw as an “I.” |

29. | Why might we prefer to use for unusual points in a regression? Explain. |

**Answer Key**

1. | |

2. | |

3. | C |

4. | C |

5. | C |

6. | |

7. | |

8. | |

9. | |

10. | |

11. | C |

12. | |

13. | |

14. | |

15. | B |

16. | |

17. | |

18. | |

19. | |

20. | B |

21. | A |

22. | C |

23. | C |

24. | C |

25. | C |

26. | B |

27. | C |

28. | |

29. |

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