A multiple regression is run with three explanatory variables, X1, X2, and X3. The p-values of their three regression coefficients turn out to be 0.07, 0.02, and 0.35, respectively, the R-square value for the regression is 0.73, and the standard error of estimate is 27.49. Which of the following will definitely be true if the regression is run again without X3?   a. The standard error of estimate will be less than 27.49.     b. The p-values of X1 and X2 will both be less 0.05.     c. The R-square value will be larger than 0.73.     d. None of these choices are guaranteed to be true.

You’ve run a regression of the effect of years of schooling on wages for a sample of 102,498 individuals. Your regression results are:   wage = 2.051    +    0.29 × Years of Schooling            (0.0802)     (0.0168)   Interpret the coefficients from this regression. (The coefficients are shown in the regression equation itself.)   The numbers in parentheses under the equation are the standard errors of the estimates for the respective coefficients. Determine whether each coefficient is statistically significant at each of the conventional significance levels.   The R2 for this regression is 0.284. Interpret the meaning of this value.

Find the multiple regression equation with weight as the response variable and the dummy variable of sex and the variable of age as the explanatory variables.

You may need to use the appropriate technology to answer this question. A regression analysis involving 45 observations relating a dependent variable and two independent variables resulted in the following information. ý = 0.406 + 1.3385X, + 2X2 The SSE for the above model is 43. When two other independent variables were added to the model, the following information was provided. ý = 1.9 – 3X + 12X2 + 4Xg + 8x, This model's SSE is 36. At a 0.05 level of significance, test to determine if the two added independent variables contribute significantly to the model. State the relevant null and alternative hypotheses. O Ho: One or more of the parameters is not equal to zero. H₂: B₁ = B₂= B3 =B4 = 0 O Ho: One or more of the parameters is not equal to zero. H₂: B3 =B4 = 0 O Ho: B3 = P4 = 0 H₂: None of the parameters are equal to zero. ⒸH₁: B3 =B₁ = 0 H: One or more of the parameters is not equal to zero. O Ho: B₁ = P₂ = B3 =B4 = 0 H: One or more of the parameters is not equal to zero. ✔ Find…