Provide an appropriate response. The data below are the average one-way commute

Question

Provide an appropriate response. The data below are the average one-way commute times (in minutes) for selected students and the number of absences for those students during the term. Find the equation of the regression line for the given data. What would be the predicted number of absences if the commute time was 40 minutes? Is this a reasonable question? Round the predicted number of absences to the nearest whole number. Round the regression line values to the nearest hundredth.

Commute time (min), x 72 85 91 90 88 98 75 100 80

Number of absences. y 3 7 10 10 8 15 4 15 5

: a) yˆ=0.45x30.27; 12 absences; Yes, it is reasonable.

b) yˆ=0.45x+30.27; 48 absences; Yes, it is reasonable.

c) yˆ=0.45x+30.27; 48 absences; No, it is not reasonable. 40 minutes is well outside the scope of the model.

d) yˆ=0.45x30.27; 12 absences No, it is not reasonable. 40 minutes is well outside the scope of the model.

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -30.267733 + 0.44853607 x
Sample size: 9
R (correlation coefficient) = 0.98000515
R-sq = 0.96041009
Estimate of error standard deviation: 0.93393518

Parameter estimates:

Analysis of variance table for regression model:

Hence,

Regression equation will be:

yˆ=0.45x30.27

For x = 40, y = -12 which is not reasonable.

Therefore,

Option D is correct.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -30.267733 2.9954727 0 7 -10.104493 <0.0001 Slope 0.44853607 0.034420112 0 7 13.031221 <0.0001

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