For observed data y=(y1,…,yn)y=(y1,…,yn) with  n=21n=21, the above linear regression model was fitted in R, with the following output:  >n = 21 >xi = seq(0, n-1,1)/(n-1) >p1 =2*xi-1 >p2 =6*xi^2- 6*xi+1-1/(n-1) > summary(lm(y ~ p1+p2)) Call: lm(formula = y ~ p1 + p2) Residuals:     Min      1Q  Median      3Q     Max -0.5258 -0.2153  0.0813  0.1770  0.4669 Coefficients:              Estimate Std. Error t value Pr(>|t|) (Intercept) -0.004238   0.063450  -0.067    0.947 p1           1.181260   0.104784  11.273 1.37e-09 *** p2          -0.953388   0.129422  -7.366 7.77e-07 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.2908 on 18 degrees of freedom Multiple R-squared:  0.9097,    Adjusted R-squared:  0.8997 F-statistic: 90.68 on 2 and 18 DF,  p-value: 3.989e-10   Write this linear regression model in the vector form and answer the following questions, using the above R output where necessary.

The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ŷ = 82.1 + 2.23x, + 1.70x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.345. (a) Compute and interpret R2 and R_2. (Round your answers to three decimal places.) . Adjusting for the number of independent variables in the model, the The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is

Complete the missing information for this regression model.  Note:  N=26N=26. (Except for P-values, report all values accurate to 3 decimal places.  For P-values, report accurate to 4 decimal places.) ˆYY^ = 26.759 + 0.818X10.818X1 −- 2.999X22.999X2 + X3X3     2.382   0.547   1.674   0.734       Standard Errors     11.234   1.495               t-ratios                 0.0991       P-values

The authors of the paper "Predicting Yolk Height, Yolk Width, Albumen Length, Eggshell Weight, Egg Shape Index, Eggshell Thickness, Egg Surface Area of Japanese Quails Using Various Egg Traits as Regressors"t used a multiple regression model with two independent variables where y = quail egg weight (g), X, = egg width (mm), and X2 = egg length (mm). The regression function suggested in the paper is -21.658 + 0.828x, 0.373x2. + (a) What is the mean egg weight for quail eggs that have a width of 20 mm and a length of 48 mm? (Enter your answer to three decimal places.) (b) Interpret the value of B,. O When width is fixed, the mean increase in weight associated with a 1-mm increase in length is 0.373 g. When length is fixed, the mean increase in weight associated with a 1-mm increase in width is 0.373 g. O When length is fixed, the mean increase in weight associated with a 1-mm increase in width is 0.828 g. O When width is fixed, the mean increase in weight associated with a 1-mm increase…

This table reports the regression coefficients when the returns of the size-institutionalownership portfolio (columns 1 and 2) returns are regressed on three variables: a constant(column 3), the stock market returns (column 4), and the change of the value weighted discountof the closed end fund industry (column 6). Columns 5 and 7 report the corresponding t-statistics of the coefficient estimates. Note that a t-statistic with an absolute value above 1.96means the coefficient estimate is significantly different from 0 at the 1% level. Column 8reports the R square of the regressions. Column 9 reports the mean institutional ownership ofeach portfolio. The last column reports the F-statistics for a multivariate test of the null                 hypothesis that the coefficient on ΔVWD in the Low (L) ownership portfolio is equal to theHigh (H) ownership portfolio. Two-tailed p-values are in parentheses. 1. What is the main finding of this Table? 2. What is the explanation for…

This is my question! All parts please.