The Director of Undergraduate Studies at a major university gathered the followi

Question

The Director of Undergraduate Studies at a major university gathered the following sample information of 15 graduates last spring.

Student

The starting salary is reported in thousands ($000) and GPA is reported on the traditional 4-point scale. A 1 indicates the student graduated from a school of business; a 0 indicates the student graduated from one of the other schools (non-business).

1. Conduct a test of hypothesis for each independent variable. Use the 0.05 significance level. Show the 4-steps: hypothesis, test statistic, rejection rules (critical value and p-value), and decision/interpret your decision.

2. Would you recommend eliminating either of the independent variables?

3. What other independent variables would you recommend adding to improve the estimation of the salary of recent business school graduates? Name at least two.

Student

Salary (in $000) GPA Business 1 $31.50 3.245 0 2 $33.00 3.278 0 3 $34.10 3.52 1 4 $35.40 3.74 1 5 $34.20 3.52 1 6 $34.00 3.421 1 7 $34.50 3.41 1 8 $35.00 3.63 1 9 $34.70 3.355 1 10 $32.50 3.08 0 11 $31.50 3.025 0 12 $32.20 3.146 0 13 $34.00 3.465 1 14 $32.80 3.245 0 15 $31.80 3.025 0

Explanation / Answer

1)If p-value is less than 0.05 ,we reject the null hypothesis and conclude that the variable is significant

GPA - TS = 2.507 , p-value = 0.02755 < 0.05

hence GPA is significant

Business - tStat = 2.8048 p-value = 0.0159

p-value < 0.05

hence Business is also significant

2)since both variables are significant, it is not recommended to eliminate either of the independent variables

3)

SUMMARY OUTPUT Regression Statistics Multiple R 0.942253061 R Square 0.887840832 Adjusted R Square 0.869147637 Standard Error 0.472212758 Observations 15 ANOVA df SS MS F Significance F Regression 2 21.18151467 10.590757 47.49540385 1.99E-06 Residual 12 2.675818663 0.2229849 Total 14 23.85733333 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 23.44737479 3.490103226 6.7182468 0.000021392 15.84309 31.05166 15.84309 31.05166 GPA 2.774831085 1.106820738 2.5070285 0.027557702 0.363276 5.186386 0.363276 5.186386 Business 1.307058321 0.466003078 2.8048277 0.015901236 0.291725 2.322392 0.291725 2.322392

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