Question 26-30 are based on the following The table below provides the data for

Question

Question 26-30 are based on the following

The table below provides the data for a sample of 10 individuals showing the hourly earnings of the persons and their years of schooling.

Hourly Years of Earnings Schooling $17.24 15 15.00 16 14.91 8 4.50 6 18.00 15 8.29 12 19.23 16 18.69 18 7.21 12 42.06 22

The following calculations are done for you. x = 14 (x x)(y y) = 358.48 y = 16.513 (x x)² = 198 xy = 2670.3 x² = 2158

Fill in the blank cells in the following regression summary output and answer questions 26-30.

SUMMARY OUTPUT Regression Statistics Multiple R 0.8176 R Square Adjusted R Square 0.6271 Standard Error Observations 10 ANOVA df SS MS F Signif F Regression 649.02985 16.134237 0.0038586 Residual 321.81496 Total 970.84481 Coefficients Std Error t Stat P-value Lower 95% Upper 95% Intercept 6.6214 -1.3342 0.2189 -24.1031 6.435 Schooling 0.0039 2.8499

26 The prediction error for a person with 18 years of schooling is:

a -6.81

b -6.49

c -6.18

d -5.07

27 The standard error of estimate for the regression is:

a 6.342

b 7.611

c 8.22

d 8.877

28 The sample data indicates that _____% of the variations in hourly earnings is explained by years of schooling.

a 60.2%

b 66.9%

c 73.5%

d 80.9%

29 Given the standard error of slope coefficient as 0.451, the value of the test statistic to test the null hypothesis that hourly earnings is unrelated to years of education is:

a 4.016

b 3.615

c 3.326

d 3.16

30 The margin of error to build a 95% confidence interval for the population slope coefficient is:

a 1.24

b 1.22

c 1.20

d 1.04

Explanation / Answer

The underlined ones are the required fill in the blanks asked in the question.

[The data is inputed in excel and REGRESSION from data analysis present in data tab is carried out on the data with Y and X inputed in the respective boxes. The following output is obtained.]

26. The prediction error for a person with 18 years of schooling is : d) -5.07

[ As obtained in excel :

Observation Predicted Y Residuals

-5.065020202

Here, the 8th observation is the required observation having 18 years of schooling. Hence, the answer. ]

27.The standard error of estimate for the regression is: a) 6.342

[The result is shown above as excel output.]

28. The sample data indicates that _____% of the variations in hourly earnings is explained by years of schooling : b) 66.9%

[R square = 0.66852, which gives the proportion of variability of Y explained by the independent variable X.
Hence, the answer.]

29.Given the standard error of slope coefficient as 0.451, the value of the test statistic to test the null hypothesis that hourly earnings is unrelated to years of education is: a) 4.016

[Excel ouput given above.

t-stat given for Schooling is the required answer.]

Regression Statistics : Multiple R 0.817631 R Square 0.668521 Adjusted R Square 0.627086 Standard Error 6.342466 Observations 10 ANOVA df SS MS F Significance F Regression 1 649.0299 649.0299 16.13424 0.003859 Residual 8 321.815 40.22687 Total 9 970.8448 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -8.83407 6.621422 -1.33417 0.218878 -24.1031 6.434955 Schooling 1.810505 0.450739 4.016745 0.003859 0.771098 2.849912

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