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# interpretation of regression, null hypothesis, degrees of freedom

1. Each year a nationally recognized publication conducts its "Survey of America's Best Graduate and Professional Schools."

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT was performed using 25 data points and the results are shown below:

0 = -92040 1 = 228 s = 3213 R2 = .66 r = .81 df = 23 t = 6.67

Give a practical interpretation of 1 = 228.

1) Mean GMAT is estimated to increase 228 points for every \$1 increase in SALARY.
2) Mean SALARY is estimated to increase \$228 for every 1-point increase in GMAT.
3) We expect to predict SALARY to within 2(228) = \$456 of its true value using GMAT in a straight-line model.
4) The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data.

2. Which of the following is NOT true of Null hypothesis?

1) The hypothesis that the researcher would like to be true
2) Any observed difference in samples is due to chance or sampling error
3) The hypothesis being tested
4) A hypothesis about a population parameter

3. You want to test the null hypothesis that age and life satisfaction are independent. Age is coded as three groups (1= 18-29, 2=30-49, 3= 50 and over), and life satisfaction is coded as (1= very satisfied, 2= moderately satisfied, 3=neutral, 4= moderately dissatisfied, 5= very dissatisfied). What are the degrees of freedom?

1) 12
2) 15
3) 9
4) 8

#### Solution Preview

1. Each year a nationally recognized publication conducts its "Survey of America's Best Graduate and Professional Schools."

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT was performed using 25 data points and the results are shown below.

Give a practical interpretation of 1 = 228.

In the regression, salary will be the dependent variable (y) and GMAT score will be the independent variable (x). The results show that the regression ...

\$2.19