Problem 1. Show all calculations. Given a random sample with 2 variables: Y is the dependent variable and X is independent variable. Y X 4 7 8 9 LO 11 2 4 12 13 a) Compute and interpret the correlation coefficient b) Estimate the regression model Y=a + bX, coefficients ( a and b)Problem 2 Given a random sample with 2 variables: Y is the dependent variable and X is independent variable. Y is measured in inches and X is measured in minutes. Regression analysis is performed with Excel and the output is presented below. Use this output and do additional computations where necessary to answer the following questions. SUMMARY OUTPUT Regression Statistics Multiple R 0.770673129 R Square 0.593937072 Adjusted R Square 0.512724487 Standard Error 2.41331775 Observations 7 ANOVA MS F Repression 42.59377289 42.59377289 7.313362432 0.04256369 Residual 5 20.12051282 5.824102564 Total 71.71478571 Coefficients Standard Error t Stot P-value Lower 95% Upper 95% Intercept -1.815384615 3.181977106 -0.570520954 0.593006136 -9.994917166 6.364147935 X Variable 1 D.874358974 0.323318998 2.704322916 0.01256369 0.013241032 1.705476917 a) Is the model statistically significant? b) What is the explanatory power of the model? c) What is the correlation coefficient? Interpret. d) What is the slope for this regression model, its significance and 95%CI? e) Interpret the slope () Interpret the intercept - in words and graphically