Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes estimates the OLS regression testscore=640.3-4.93CS, R2=0.11, SER=8.7 (23.5) (2.02) Hint: The number in parenthesis are the standard errors. 1.Construct a 95% confidence interval for β1 , the regression slope coefficient. 2.Calculate the p-value for the two-sided test of the null hypothesis H0: β1=0 . Do you reject the null hypothesis (i) at 5% level, (ii) at 1% level. 3.Calculate the p-value for the two-sided test of the null hypothesis H0: β1=-5.0 . Without doing any calculations, determine whether -5.0 is contained in the 95% confidence interval for β1 .
Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes estimates the OLS regression
testscore=640.3-4.93CS, R2=0.11, SER=8.7
(23.5) (2.02)
Hint: The number in parenthesis are the standard errors.
1.Construct a 95% confidence interval for β1 , the regression slope coefficient.
2.Calculate the p-value for the two-sided test of the null hypothesis H0: β1=0 . Do you reject the null hypothesis (i) at 5% level, (ii) at 1% level.
3.Calculate the p-value for the two-sided test of the null hypothesis H0: β1=-5.0 . Without doing any calculations, determine whether -5.0 is contained in the 95% confidence interval for β1 .
4.Construct a 90% confidence interval for β0 .
5.Calculate the F-statistics.
6.Show the F-statistics is equal to the square of the t-statistics of the slope of the regression.
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