Armand's File Armand's Pizza Parlors 250 200 150 Quarterly Sales ($1000s) y = 5x + 60 100 R2 = 0.9027 50 o 5 10 15 20 25 30 Student Population (1000s) SUMMARY OUTPUT Regression Statistics Multiple R : 0.950122955 R Square 0.90273363 Adjusted R Square : 0.890575334 , Standard Erro 13.82931669 Observations 10 - -L. ANOVA -L- -I-. df SS MS F Significance F Regression -L - 14200 14200 1 74.24836601; 2.55E-05 Residual 8 1530 191.25 - - - - - - - - - Total 9_ 15730 - - - - - - Standard Coefficients Error t Stat P-value Lower 95% Upper 95% ; Lower 99.0% Upper 99.0% - ! !- - - - . . ." . . . . . . . . . . . . 6.50333 Intercept 60 9.22603481 6 0.000187444: 38.72473 81.27527 29.04308 90.95692 ---r Population 5 :0.580265238 8.616749; 2.54887E-05 ! 3.661906 6.338094 3.052985 6.947015 - - - - . . . .- - - - . . . . .= - - - - - - - -1. What is the estimated regression equation? 2. Perform a t test and determine whether or not x and y are related. Use a = 0.01. 3. Perform an F test and determine whether or not x and y are related. Use a = 0.01. 4. Find and interpret the coefficient of determination. Butler's File SUMMARY OUTPUT -4- - Regression Statistics Multiple R 0.95067817 - 4 - - - - -- - R Square 0.90378898 Adjusted R Square 0.87630011 Standard Error 0.57314215 -4- - - - Observations 10 - +- - ANOVA -L. Significance SS MS - - - L - - Regression 2 21.60055651 10.80027826 , 32.8783674 ; 0.00027624 1 - Residual 7 2.299443486 :0.328491927 Total 9 23.9 Coefficients Standard Error t Stat P-value Lower 95% : Upper 95% : Lower 99.0% Upper 99.0% Intercept -0.86870147 ; 0.951547725 1-0.912935257, 0.3916343 1-3.11875429, 1.38135136 1-4.19862684 , 2.4612239 - -F - Miles 0.0611346 0.009888495 6.182396959 ; 0.00045296 ; 0.03775202 ; 0.08451717 ; 0.02652998 ; 0.09573922 ; Deliveries 0.92342537 0.221113461 1 4.176251251 1 0.00415662 ; 0.40057512 ; 1.44627562 0.1496425 1 1.69720823 :1. Use the above results and write the regression equation that can be used to predict time. 2. Predict time when miles = 95 and deliveries = 5 3. At a = 0.01' test to determine if miles is a significant variable. At a = 0.01, test to determine if delivery is a significant variable. 4. At a = 0.01 level of significance, test to determine if the model is significant. That is, determine if there exists a significant relationship between the independent variables and the dependent variable. 5. Compute the coefficient of determination and fully explain its meaning