Question

5.Correlation and Simple Regression by Hand Hourly Earnings in Dollars) $35 $15 $40 $30 $55 (Years of Education) 16 14 18 12 20 Be sure to show all of your calculations and to interpret your findings. That is, while you can use R to check your work, you must show all of the calculations below "by hand." Assume that the populations are normal. Compute the sample correlation coefficient (r) between hourly earnings and vears of education for this random sample of 5 students in a class. A. B.Test the null hypothesis Ho: p 0 versus the alternative hypothesis H1.p # 0. Can you reject the null hypothesis at the 5-percent level of significance? Can you reject the null at the 1-percent level of significance? Show your work and explain. C.Use cor.test ) in R to check your work in Parts A and B above D. Use ordinary least squares (OLS) to estimate the following linear regression model by hand: E. Use R to replicate the results from Part D using the 1m ) command as shown in lecture. Report your results in tabular form using the package stargazer. Is the slope coefficient statistically different from zero at the 10-percent level of significance? Is it statistically different from zero at the 5-percent level of significance? Show your work Precisely interpret the exact meaning of the estimated slope coefficient in this particular case? What is the predicted hourly wages of someone with 13 years of education, based on the regression results? Show your work and explain. F. and explain. G. H.

Answer 1

and puty thu val,oe hau +55+429) 150 0.8)349 (approx) (B) The nul hypoheis obedy Bu t-Stabi'she Te 2. The Calculatedt ouldbe o-81344 V5-2 1-6 813 2、4-224 Tt wou ld be a ton-taild