Instructions We have a theoretical regression model: y(i)= BO + B1.x1(i) + B2 x2(i) + B3-x3(i) + e(i). Note that the third explanatory variable is a dummy variable. Use the following multiple linear regression results by Excel in the next page) to aid your answers. Regression Statistics R Square ? y = dependent variable Adjusted R ? x1 = independent variable (quantitative) Square Standard Error ? X2 = independent variable (quantitative) Observations 100 x3 = independent variable (dummy: 0 or 1) ANOVA df SS MS F Significance F Regression ? ? 264567.209 ? 0.00000 Residual ? 179283.475 1867.536 Total ? 972985.103 Coefficients Std. t Stat P-value Lower Upper 95% Error 95% Intercept -10.87525 19.82674 -0.54851 0.58461 -50.23102 28.48051 X1 -2.33423 0.14894 -15.67258 0.00000 -2.62987 -2.03859 X2 4.51956 0.44279 10.20691 0.00000 3.64062 5.39850 X3 46.10008 8.82841 5.22179 0.00000 28.57582 63.62435 (a)[2] Based on the regression results, copy SST and SSE. Then, calculate SSR. Calculate the degrees of freedom for these three statistics: df(SST), df (SSR), and df (SSE). (b)[2] Give an equation for the coefficient of multiple determination R2 in terms of SSR and SST. Give another equation for R2 in terms of SSE and SST. Calculate and comment on R2. (c) [2] Give an equation for adjusted R2. Calculate R (adj). (d)[2] Give an equation for and calculate the F-statistic. Sketch the corresponding p-value with all necessary information, including the degrees of freedom. By looking at the p-value of the F- statistic, make a comment on the overall significance of the regression. (e)[2] Using all results, specify the sample regression equation in the following 3-line format: y = b. b1 x1 b2.x2 b3x3 (t-1)* (t-2)** (-3)*** n = ?; R2 = ?; R (adj) = ?; F= ? [p-value]** Note that: *** for p-value