1. See the plots on the next page labeled a and b. For each, identify the existence of the following for each plot if applicable. (5 ea.)

Linear relationship Outlier(s) High-leverage case(s) Negative relationship

a.

b.

Please refer to the attached regression output. Here we are using years of experience, college GPA, and company entrance score to predict employee salaries at a local firm.

2. We would conclude that the overall model (using all three explanatory variables) is statistically significant at the .05 level. (3)

a. true b. false

c. We should perform partial t-tests. (True / False) (2) d. Which of the variables are significant predictors? (4)

3. The most useful predictor in the presence of the other explanatory variables is __________. (2)

4. Multicollinearity is (3)

  1. severe.
  2. mild.
  3. nonexistent.

5. Which of the following combinations would be expected to yield the highest pay? Values are years, GPA, and score. (3)

  1. 5, 3.7, 80
  2. 7, 3.2, 85
  3. 8, 3.6, 85
  4. 5, 3.8, 85
  1. The percentage of variation in salary explained by the three x-variables is ______. (3)
  2. The model in Summary Output 2 uses only entrance score to predict salary.
  1. The sample slope = ________. (2)
  2. The sample intercept = ________. (2)
  3. The correlation is __________. (positive or negative) (2)
  4. The percentage of variation in salary explained by score is ____. (2)
  5. This a useful model. (True / False) (3)

8. For the following regression models (computed using the same set of data), which statement is most appropriate? (5)

Model 1

Model 2

Model 3

X-variables

6

4

3

R2

.9344

.9277

.8761

Adjusted R2

.9058

.9133

.8497

MSE

5867.53

5746.09

5844.78

a.

b.

  1. Model 1 performs the best in all areas.
  2. Model 3 performs better than Model 2.
  3. We would most likely prefer Model 1.
  4. We would most likely prefer Model 2.
  5. We would most likely prefer Model 3.

SUMMARY OUTPUT 1

Regression Statistics Multiple R

R Square

Adjusted R Square

Standard Error Observations

ANOVA

Regression Residual Total

Intercept Years GPA Score

0.686507 0.4712919

0.3655502 18.962716 19

Significance df SS MS F F

3 15 18

Coefficients -59.69295 -0.510186

24.510667 0.7600061

4808.020459 5393.769015 10201.78947

Standard

Error

38.48117376 1.100900645 12.31973076 0.295486746

1602.673 4.457014 359.5846

t Stat P-value -1.55122 0.141687 -0.46343 0.649712

1.989546 0.065194 2.572048 0.021248

0.019857133

Correlation Matrix

Salary

1 Years 0.192517816 GPA 0.484367567

Years GPA

1 0.280138

Score

1

Salary

Score

SUMMARY OUTPUT 2

Regression Statistics

0.575980821

0.341399

0.226652 1

Multiple R R Square

Adjusted R Square

Standard Error Observations

ANOVA

Regression Residual Total

Intercept Score

0.5759808 0.3317539

0.2924453 20.025434 19

Significance df SS MS F F

1 3384.483506 17 6817.305968 18 10201.78947

Standard Coefficients Error

8.103183 18.48029361 0.8430371 0.290189996

3384.484 401.018

t Stat

0.438477 2.905121

8.43973 0.009855012

P-value

0.666562 0.009855

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