Chapter 20, Problem 1E

Graduate earnings Does attending college pay back the investment? What factors predict higher earnings for graduates? Money magazine surveyed graduates, asking about their point of view of the colleges they had attended (Money’s Best Colleges at new.time.com/money/best-colleges/rankings/best-colleges/). One good predictor of early career earnings ($/year) turned out to be the average SAT score of entering students. Here are the regression model and associated plots. Write the regression model and explain what the slope coefficient means in this context. Response variable is: Earn

R squared = 30.7%

s = 5603 with 706 – 2 = 704 degrees of freedom

Variable	Coefficient	SE(Coeff)	t-ratio	P-value
Intercept	14468.1	1777	8.14	<0.0001
SAT	27.2642	1.545	17.6	<0.0001

To determine

Write the regression model.

Explain the slope coefficient means in the context.

Answer to Problem 1E

The regression model is,

$\widehat{\text{Earn}}=14,468.1+27.262\left(\text{SAT}\right)$

The slope coefficient means in the context is the graduates earn approximately $27.26 per year more for each additional point in SAT score.

Explanation of Solution

Given info:

A output shows the regression model and associated plots.

Calculation:

The linear regression model is,

$\widehat{y}=b_0+b_{1}x$

Where, $\widehat{y}$ represents the predicted variable, x represents the predictor variable $b_0$ represents intercept and $b_1$ represents slope.

From the output, it can be observed that the predicted variable is Earn, predictor variable is SAT score, intercept is 14,468.1 and the slope is 27.262.

Thus, the linear regression model that predicts from SAT score is,

$\widehat{\text{Earn}}=14,468.1+27.262\left(\text{SAT}\right)$

Here, the slope coefficient means in the context is the graduates earn approximately $27.26 per year more for each additional point in SAT score.