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A fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins
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.
| Years of education | Winnings |
| 12 | 500 |
| 16 | 400 |
| 12 | 600 |
| 16 | 500 |
| 14 | 500 |
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?
| a. |
decrease by $12.5 |
|
| b. |
decrease by $37.5 |
|
| c. |
decrease by $50 |
|
| d. |
decrease by $62.5 |
|
| e. |
decrease by $25 |
Expert Solution
The predicted change in the winnigs when the education of the winner increases by an year is option e) a decrease by $25. Since the slope of the regression equation is -25, which depicts a decrease in winning by 25.
? = -25X + 850 (Regression equation)
Explanation:
X represents Years of education and Y represent the winnings (in $).
|
X |
Y |
|
12 |
600 |
|
12 |
500 |
|
14 |
500 |
|
16 |
500 |
|
16 |
400 |
|
M = 14 |
M = 500 |
Calculation Summary
Sum of X = 70
Sum of Y = 2500
Mean X = 14
Mean Y = 500
Sum of squares (SSX) = 16
Sum of products (SP) = -400
|
X-MX |
Y-MY |
(X-MX)2 |
(X-MX)*( Y-MY) |
|
-2 |
100 |
4 |
-200 |
|
-2 |
0 |
4 |
0 |
|
0 |
0 |
0 |
0 |
|
2 |
0 |
4 |
0 |
|
2 |
-100 |
4 |
-200 |
|
SS = 16 |
SP = -400 |
Regression Equation = ? = bX + a
b = SP/SSX = -400/16 = -25
a = MY - bMX
= 500 - (-25*14)
= 850
? = -25X + 850
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