near regression yields βˆ1 = 0 , Show that R2 = 0. (b) A linear regression yields R2 = 0. Does this imply that βˆ1 = 0?
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(a) A linear regression yields βˆ1 = 0 , Show that R2 = 0.
(b) A linear regression yields R2 = 0. Does this imply that βˆ1 = 0?
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- A particular article presented data on y = tar content (grains/100 ft³) of a gas stream as a function of x₁ = rotor speed (rev/min) and x₂ = gas inlet temperature (°F). The following regression model using X₁, X2, X3 = ×₂² and ×4 = X₁X₂ was suggested. (mean y value) = 86.5 – 0.121x₁ +5.07x2 - 0.0706x3 + 0.001x4 (a) According to this model, what is the mean y value (in grains/100 ft³) if x₁ = 3,400 and x₂ = 55. grains/100 ft³ (b) For this particular model, does it make sense to interpret the value of ₂ as the average change in tar content associated with a 1-degree increase in gas inlet temperature when rotor speed is held constant? Explain. Yes, since there are no other terms involving X2. O Yes, since there are other terms involving X₂. ● No, since there are other terms involving X2. O No, since there are no other terms involving X2.The annual expenditure for cell phones varies by the age of an individual. The average annual expenditure E(a) (in $) for individuals of age a (in years) is given below:a: 20, 30, 40, 50, 60, 70E(a): 502, 658, 649, 627, 476, 2131. Use quadratic regression to find the model that best represents the data.2. At what age is the yearly expenditure for cell phones the greatest? Round the answer to the nearest year. YOU MUST SHOW THE WORK FOR THIS PART!Use the linear regression model yˆ=−24.8x+564.38 to predict the y-value for x=63.
- Use the linear regression model yˆ=−21.9x+927.93 to predict the y-value for x=37.The volume (in cubic feet) of a black cherry tree can be modeled by the equation y=−51.9+0.3x1+4.9x2, where x1 is the tree's height (in feet) and x2 is the tree's diameter (in inches). Use the multiple regression equation to predict the y-values for the values of the independent variables.A weight-loss clinic wants to use regression analysis to build a model for weight loss of a client (measured in pounds), Two variables thought to affect weight loss are client's length of time on the weight-loss program and time of session These variables are described below: Y-BO+B1'X+82'D 83'X'D+E Y-Weight loss (in pounds) X- Length of time in weight-loss program (in months) D-1 if morning session. O if not in terms of the Bs in the model, what is the difference between the weight loss of an individual who has spent 3 months in the program when attending the morning session, and an individual who has spent 2 months in the program when attending the evening session? OB1+83 OB1+82-83 OB1+82+283 O81+82+383
- For10 observations on supply (X) and price (Y) the following data are obtained ΣΧ-130, ΣΧ-2280, ΣΥ-5506 , ΣΧΥ-3467, ΣΥ-220 Obtain regression line Y on X and estimate supply when price is 16.It has been hypothesized that overall academic success for first-year college students as measured by grade point average (GPA) is a function of IQ scores = X1, and hours spent studying each week = X2. Suppose the regression equation is: Y = -5.7 + 0.02X1 +0.5X2 1) What is the predicted GPA for a student with an IQ of 100 and 40 hours spent studying per week? 2)Will the independent variables be endogenous? State what it means by endogenous, and explain why that will be the case. 3) If you have a choice to change the variables or add/drop variables, what would be your set of independent variables, and explain why you chose those variables.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 ý = 82.3 + 2.29x, + 1.90x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.415. (a) Compute and interpret R? and R 2. (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 653 x . 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 R,2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis (is preferred since both R2 and R.2 show an increased v v…
- A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. A linear regression was performed on these data, and the result is the linear regression equation Yi=−0.840+1.4108Xi. Determine the coefficient of determination,r2,and interpret its meaning. Determine the standard error of the estimate. How useful do you think this regression model is for predicting opening weekend box office gross? Can you think of other variables that might explain the variation in opening weekend box office gross?A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. A linear regression was performed on these data, and the result is the linear regression equation Yi=−1.254+1.3968Xi. Complete parts (a) through (d). a. Determine the coefficient of determination,r2,and interpret its meaning. b. Determine the standard error of the estimate. c. How useful do you think this regression model is for predicting opening weekend box office gross? d. Can you think of other variables that might explain the variation in opening weekend box office gross?Exercise 4 In this regression we presented the results of the consumption fitted to the income in the period 1980-2005. We divide the data in two periods as 1980-1992 and 1993-2005. Decide if there is a structural change in the consumption-income regression in the two periods. The results for all data are as follows cons = 179 + 0.85 Income RSSfull = 265277 The results for 1980-1992(1) and 1993-2005 (2) are as follows 143 - 0.85 Income RSSfull = 13310 (1) cons = cons = 110 + 0.18 Income RSSfui = 163505 (2) fll
