A fan of television game shows has observed that, in general, the more educated
ID: 3312658 • Letter: A
Question
A fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief she gathers data about the last five winners of her favorite game show. She records their winnings in dollars and the number of years of education. The data are as follows.
She estimated a regression model using winnings as the dependent variable (Y) and years of education as the independent variable (X). She used the ordinary least squares estimator. What is the predicted change in winnings when the education of the winner increases by a year?
decrease by $50
decrease by $75
decrease by $62.5
decrease by $25
decrease by $37.5
Years of education Winnings 12 500 16 300 12 600 16 600 14 500Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: Winnings
Independent Variable: Years of education
Winnings = 850 - 25 Years of education
Sample size: 5
R (correlation coefficient) = -0.40824829
R-sq = 0.16666667
Estimate of error standard deviation: 129.09944
Parameter estimates:
Analysis of variance table for regression model:
From the regression output, we can see that the slope is -25.
Hence,
Predicted change in winnings decreases by $25 when the education of the winner increases by a year.
Option D is correct.
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 850 455.52168 0 3 1.8659924 0.1589 Slope -25 32.274861 0 3 -0.77459667 0.495Related Questions
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