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) 4.2100541 1.8661683 2.256 0.02909 *
Ascent 0.0020805 0.0005909 3.521 0.00101 **
What is the fitted regression model?
2.
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 Y = Time (expected trip time o hike the peak, in hours) on X = Ascent (in feet), and the fitted model is
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
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.
) 0.63 hours
) Somewhere between 0 and 18 hours, but we can't be more specific
) 4.8 hours
) 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).
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 Y = Time
(expected trip time to hike the peak, in hours) on X = Ascent (in feet) results in a standard error of regression of 2.496. Interpret this value.
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 Y = Time (expected trip time to hike the peak, in hours) on X = Ascent (in feet) results in the residual plots below. Are there any outliers in this situation? If so, identify these points and explain what leads you to believe they are outliers.
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 Y = Time (expected trip time to hike the peak, in hours) on X = Ascent (in feet) results in the scatterplot and residual plots below. Are there any influential points in this situation? If so, identify these points and explain what leads you to believe they are influential.
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 Y = Time (expected trip time to hike the peak, in hours) on X = Ascent (in feet) results in the scatterplot and residual plots below. Are the conditions for inference met in this case? Make sure you discuss each condition.
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 Y = Time (expected trip time to hike the peak, in hours) on X = Ascent (in feet) results in the scatterplot and residual plots below. Do you think a transformation for the explanatory or response variable is needed here? Explain your answer. If you think a transformation is needed, suggest a specific transformation and explain why you recommend it specifically.
11. F P o (i a n fi
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 Elevation (in feet) f each peak, Difficulty rating (on a 2 to 7 scale with 7 being the most difficult), Ascent n feet), Length of a round-trip (in miles), and expected hike Time (in hours). Below is scatterplot matrix. This is a matrix that contains a scatterplot for each pair of
umerical variables in the data set. For instance, the graph in the second column of the rst row shows a scatterplot with Elevation on the x axis and Time on the y axis.
ased on these plots, which variable is the best single predictor of Time?
) Elevation
) Ascent
) Length
12.
Cholesterol levels are measured on a sample of 21 volunteers. HDL (high-density
lipoprotein, or “good” cholesterol) is regressed on total cholesterol (Chol). Below is some R output from a regression model. Write down the least-squares regression line for these data.
> summary(chol.lm) Call:
lm(formula = HDL ~ Chol, data = HDL)
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.
lipoprotein, or “good” cholesterol) is regressed on total cholesterol (Chol). Below is some R output from a regression model. Interpret the slope of the model in context.
14.
lipoprotein, or “good” cholesterol) is regressed on total cholesterol (Chol). The fitted model is
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 (Chol). The fitted odel is
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?
) 32.5 mg/dl
) 56.8 mg/dl
) 57.2 mg/dl
) 304.3 mg/dl
16.
lipoprotein, or “good” cholesterol) is regressed on total cholesterol (Chol), which results in the residual plots below. Are there any outliers in this situation? If so, identify these points and explain what leads you to believe they are outliers.
17.
lipoprotein, or “good” cholesterol) is regressed on total cholesterol (Chol), which results in the scatterplot and residual plots below. Are there any influential points in this situation? If so, identify these points and explain what leads you to believe they are influential.
18.
lipoprotein, or “good” cholesterol) is regressed on total cholesterol (Chol), which results in the scatterplot and residual plots below. Are the conditions for inference met in this case? Make sure you discuss each condition.
19.
lipoprotein, or “good” cholesterol) is regressed on total cholesterol (Chol), which results in the scatterplot and residual plots below. Do you think a transformation for the explanatory or response variable is needed here? Explain your answer. If you think a transformation is needed, suggest a specific transformation and explain why you recommend it specifically.
20.
t
p
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 reasonable, roblematic, or you can't judge (from the plot shown)?
) Reasonable
) Problematic
) Can't judge
21.
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 reasonable, roblematic, or you can't judge (from the plot shown)?
22.
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 reasonable, roblematic, or you can't judge (from the plot shown)?
23.
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 reasonable, roblematic, or you can't judge (from the plot shown)?
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 reasonable, roblematic, or you can't judge (from the plot shown)?
25.
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 reasonable, roblematic, or you can't judge (from the plot shown)?
26.
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 reasonable, roblematic, or you can't judge (from the plot shown)?
27.
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 reasonable, roblematic, or you can't judge (from the plot shown)?
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 standardized residuals (rather than residuals) when looking
for unusual points in a regression? Explain.
Answer Key
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