Obtain the iterative weighted least squares for estimating the regression coefficients Yi ~f (yi; Bi) = B²y₁e-B₁y₁ log i = log Ey; = B₁ + B₂x₁
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- The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (x2). The estimated regression equation was ŷ = 82.4 + 2.23x1 + 1.40x2. The computer solution, based on a sample of eight weeks, provided SST = 25.5 and SSR = 23.495.(Note: SST = SS yy ) (a)Compute and interpret R2 and Ra2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (??) . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (??) . (b)When television advertising was the only independent variable, R2 = 0.653 and Ra2 = 0.595. Is the multiple regression model more preferable over the simple regression model? Explain. Multiple…A multiple regression model was fit to predict domestic gross for movies based off of the production budget, opening weekend gross and number of stars. The overall F test p-value equals 0.252. What conclusion can you make at alpha = 0.05? All of the variables contribute to the model. At least one of the variables contributes to the model. O None of the variables contribute to the model.The following estimated regression equation was developed for a model involving two independent variables. ý = 40.7 + 8.63x, + 2.71.x, After x 2 was dropped from the model, the least squares method was used to obtain an estimated regression equation involving only X 1 as an independent variable. ŷ = 42.0 + 9.01x a. In the two independent variable case, the coefficient x 1 represents the expected change in Select v corresponding to a one unit increase in Select v when Select v is held constant. In the single independent variable case, the coefficient x 1 represents the expected change in Select v corresponding to a one unit increase in Select v b. Could multicollinearity explain why the coefficient of x 1 differs in the two models? Assume that x1 and x2 are correlated. Select
- Using 81 quarterly observations on the growth rate of employment (Y) and the growth rate of output (X), the following regression results are obtained by ordinary least squares (t = 1, 2,...,81): -0.002+0.105X+0.730Y-1+0.063X-1, (0.001) (0.014) (0.045) (0.016) BG 1.100 [0.363], WH=1.474 [0.175], RESET = 0.081 [0.777], R² = 0.8827, SSR 0.00061, -0.002+0.086(X+X-1)+0.711Y-1, (0.001) (0.011) (0.045) R² = 0.8767, SSR = 0.00065. is the fitted value of the regression; figures in parentheses are the standard errors of the estimated coefficients; R² is the coefficient of determination; SSR is the sum of squared residuals; BG is the Breusch-Godfrey test for fourth-order autocorre- lation; WH is White's test for heteroskedasticity; RESET is Ramsey's regression specification error test; figures in square brackets are the p-values of BG, WH and RESET. Test the null hypothesis that the coefficients on X and X-1 in the first regres- sion are equal against the alternative hypothesis that they are not…Observations are taken on sales of a certain mountain bike in 24 sporting goods stores. The regression model was Y= total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors' advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit). (a) Fill in the values in the table given here. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "O" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.) Predictor Coefficient SE tcalc P-value Intercept 1,254.2 300.2 FloorSpace 11.310 1.69 Competing Ads -6.260 3.999 Price -0.14748 0.08280 (b-1) What is the critical value of Student's tin Appendix D for a two-tailed test at a = 01? (Round your answer to 3 decimal places.) t-value (b-2) Choose the correct option. Only FloorSpace differs significantly from zero. O Only Price differs significantly from zero. O Only CompetingAds differs significantly from…Sports scientists want to use nuclear magnetic resonance spectroscopy, NMR, to predict the muscle fibre composition in the thighs of athletes. They obtained the data in the screenshot, which contains three variables: FTF – the percentage of fast twitch fibres in the muscle. T1 – the T1 relaxation time measured in ms. T2 – the T2 relaxation time measured in ms. Perform a multiple linear regression using the model FTF = b0 + b1T1 + b2T2. i) What are the values of the three coefficients in the equation? ii) What is the F statistic and P value for the regression? Do these indicate that the regression is significant? iii) Does adding the other NMR relaxation time, T2, to the predictive equation significantly improve the ability of NMR spectroscopy to predict muscle fibre type? Explain your conclusions.
- Consider the multiple regression model Y₁ = Bo + B₁x1₁j + B₂x2j+B3 x 3j+ €j under the usual assumptions labelled A1, A2, A3, A4, A5, A6. Briefly explain which type of graphs are performed in the analysis of residuals.Observations are taken on sales of a certain mountain bike in 25 sporting goods stores. The regression model was Y= total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors' advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit). (a) Fill in the values in the table given here. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.) Coefficient Predictor Intercept FloorSpace Competing Ads Price p-value SE 351.9 1.74 tcalc 1,219.0 11.002 -6.021 3.932 -0.14944 0.08582 (b-1) What is the critical value of Student's tin Appendix D for a two-tailed test at a = .01? (Round your answer to 3 decimal places.) t-value =You are given a set of data (xj, Yi) for linear regression analysis and find out these data are not linearly related by plotting (x¡, Yi) with graphical analysis. After using log transformation of data from (x¡ , yi) to (X¡ = log X¡ , Y¡ = log yi ) and a linear fitting line were derived, Y = A + BX, for the power-law relationship y = k x". You tried to find the power-law equation's kand n by transforming back from A and B in that linear relation equation Y = A + BX. Which one of the below can be the correct result? There might be more than one correct answer; please select all of the correct answers. O logA=k O n= logB O 10A=K O en=B n = B O A=logK O eK=A O eB=n
- In a comprehensive road test on new car models, one variable measured is the time it takes a car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is conducted on a random sample of 129 new cars. TIME60: y = Elapsed time (in seconds) from 0 mph to 60 mph MAX: x = Maximum speed attained (miles per hour) The simple linear model E(y) = Bo + B1x was fit to the data. Computer printouts for the analysis are given below: NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME60 PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S T CONSTANT 187171 0.63708 29.38 0.0000 0.0000 MAX -0.08365 0.00491 -17.05 0.6960 0.6937 R-SQUARED RESID. MEAN SQUARE (MSE) 1.28695 ADJUSTED R-SQUARED STAND ARD DEVIATION 113444 SOURCE DF MS F REGRESSION 374.285 0.0000 374.285 1.28695 290.83 RESIDUAL 127 163.443 TOTAL 128 537.728 CASES INCLUDED 129 MISSING CASES 0 Fill in the blank: "At a =.05, there is between maximum speed and acceleration time." O sufficient evidence of a…A regression function used to examine the factors affecting the chief executive officer salary in financial, manufacturing, utilities and transportation sector is given as below. Figures in parentheses are standard errors. Ln Y = 4.59 +0.257 log(X) + 0.158 D₁ +0.181D21 -0.283D31 se = (0.30) (0.032) (0.089) (0.085) (0.099) n = 209, R² = 0.357 Where Y = salary (in thousands) X₁ = annual sales D₁- D₂= D₂= (1, financial sector otherwise lo, manufacturing sector otherwise utililities sector otherwise Interpret the coefficient for D₂ Compute the approximate percentage difference in estimated salary between the utilities and transportation sector, holding annual sales fixed. Is the difference statistically significant at 1% level?Data was gathered from a random sample of young mothers between the ages of 15 and 19 years, and the relationship between the mother's age (measured in years) and the baby's birth weight (measured in grams) was observed to be linear, with r= 0.88. Further, the regression equation to predict a baby's birth welght based on the mother's age was found to be: Predicted birth weight = -1163.45 + 245.15(age). Based on this information, which one of the following statements is incorrect? O The predicted birth weight for a baby whose mother is 15 years old is 4840.7 grams. O If weight was measured in pounds instead of grams, the value of rwould still be 0.88. O If we switch the variables so that age is the response variable and birth weight is the explanatory variable, r would still be 0,88. O If a mother's age is 25 years, we would not want to use the regression equation to predict the baby's birth weight since this would be considered extrapolation. O Becauseris 0.88, we would consider the…
