Question

Regression Statistics Multiple R 0.72213 R Square 0.52148 Adjusted R Square 0.44172 Standard Error 47.46341 Observations 15 Sales = 306.526 - 24.975(Price) + 74.131(Advertising) ANOVA Ss Significance F 0.01201 MS 14730.013 2252.776 Regression Residual Total 6.53861 29460.027 27033.306 56493.333 t Intercept Price Coefficients 306.52619 -24.97509 74.13096 Standard Error 114.25389 10.83213 25.96732 Stat 2.68285 -2.30565 2.85478 P-value 0.01993 0.03979 0.01449 Lower 95% 57.58835 -48.57626 17.55303 Upper 95% 555.46404 -1.37392 130.70888 Advertising

Im having a hard time solving R^2 WITHOUT using EXCEL. I know the answer is 29460.0/56493.3= .52493

But where do you get 29460.0 and 56493.3

Answer 1

I have given the formula for calculating ESS and TSS . Using these formulas in the data you will get the value of ESS and TSS .

(Page No. Date : 11 Explained Sum of squares - Ess Total Sum of squares TSS Ess= R = I- RSS (Residual stem of Squares) TSS RSS = RSS = 2 2 2 (xi - A) 2 TSS = 3 (vi_y² = In this model {x;'2_ny22 Y;= V = Ple Sales sales = both ( Price) + b2 (Adventining I FOR Example 350 460 206526-24.975 (5:50) + 74.131 (33) = 413.995. 206.526 - 24.975/7.50)+74.131 (313) = 863.846 Similarly you of the given ein equation can find all the values data then put the value to to get Rss o TSS can be find by using formula from equation . Then Substitute the calue in the formula R2= I- RSS - EST TSS By further Calculating using Calculation, you 29460027 = 0.52148 will get ESS=29460.027 56493.333 T55= 56495333