Question

5 A researcher studies the relationship between SAT scores, the test-takers family income (Income), and his/her grade pointa-3. Find the value of the test statistic for Income. (Round your answer to 3 decimal places.) Answer is complete but not enta-6. Choose the hypotheses to determine whether GPA is individually significant. 10 Ho: B20; HA B2 > 0 Ho: B20; HA B2 < O о нa-9. At the 5% significance level, is GPA individually significant? Yes, since we reject the null hypothesis. 10 points Yes,5 b-3. Find the p-value 10 p-value 0.01 points 0.01 sp-value < 0.025 0.025 p-value 0.05 0.05sp-value < 0.10 eBook pvalue 0.10

SAT

Income

GPA

1651

47000

2.79

1581

34000

2.97

1790

90000

3.48

1626

60000

2.5

1754

113000

2.92

1754

71000

3.76

1706

105000

2.8

1765

59000

3.26

1786

50000

3.89

1686

27000

3.67

1790

107000

3.31

1707

109000

3.16

1804

81000

3.73

1712

62000

3.21

1607

72000

2.8

1738

63000

3.7

1790

55000

3.86

1796

64000

3.91

1547

47000

2.63

1692

89000

2.98

1711

42000

3.45

1689

70000

3.06

1740

118000

2.88

1940

113000

3.96

0 0
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Answer #1

applying Regression":

Regression Statistics
Multiple R 0.9300
R Square 0.8649
Adjusted R Square 0.8520
Standard Error 32.4902
Observations 24
ANOVA
df SS MS F Significance F
Regression 2 141927.9571 70963.9786 67.2254 0.0000
Residual 21 22167.8762 1055.6132
Total 23 164095.8333
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1104.2580 54.7524 20.1682 0.0000 990.3941 1218.1218 990.3941 1218.1218
Income 0.0017 0.0003 6.7696 0.0000 0.0012 0.0022 0.0012 0.0022
GPA 150.9920 15.0931 10.0040 0.0000 119.6042 182.3798 119.6042 182.3798

a-3)test statistic for Income =6.770

a-4) p value <0.01

a-7) test statistic for GPA =10.004

a-8) p value <0.01

b-2) test statistic F =67.225

b-3) p value <0.01

c-1) predicted SAT score =1769.10

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