Consider the two regressions models: ŷ Bo + Â₁×1 + ß₂x2 + B3X3 + B₁X4 + B5X5, where n-66 and R²=0.7 and ŷ = ß0 + Â₁×1 + ß₂x2, where n=66 and R²=0.1 Calculate the F-statistic for the joint test Ho : B3 = B4 = B5 = 0. Round to two decimal places
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![Consider the two regression models:
1. \(\hat{y} = \hat{\beta}_0 + \hat{\beta}_1 x_1 + \hat{\beta}_2 x_2 + \hat{\beta}_3 x_3 + \hat{\beta}_4 x_4 + \hat{\beta}_5 x_5\), where \(n = 66\) and \(R^2 = 0.7\).
2. \(\hat{y} = \hat{\beta}_0 + \hat{\beta}_1 x_1 + \hat{\beta}_2 x_2\), where \(n = 66\) and \(R^2 = 0.1\).
Calculate the F-statistic for the joint test \(H_0: \beta_3 = \beta_4 = \beta_5 = 0\). Round to two decimal places.
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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 (x,) and newspaper advertising (x,). The estimated regression equation was ý = 83.3 + 2.24x, + 1.30x2. The computer solution, based on a sample of eight weeks, provided SST 25.2 and SSR = 23.455. %D (a) Compute and interpret R² and R,. (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, R = 0.653 and R, = 0.595. Do you prefer the multiple regression results? Explain. %3D 2 Multiple regression analysi v ---Select--- ipreferred since both R2 and R, show ---Select--- O…Using 23 observations on each variable, a computer program generated the following multiple regression model. y = 65.5 +9.56x1+3.27x2-4.23x3– 9.23x4 If the standard errors of the coefficients of the independent variables are, respectively, 3.44, 2.30, 2.76, and 4.99, can you conclude that the independent variable x, is needed in the regression model? Let B1, B2, Ba denote the coefficients of the 4 variables in this model, and use a two-sided hypothesis test and significance level of 0.10 to determine your 4 .../ answer. (a) State the null hypothesis H, and the alternative hypothesis H,. H, : 0 H, : 0 (b) Determine the type of test statistic to use. Degrees of freedom: D=0 OSO (c) Find the value of the test statistic. (Round to two or more decimal places.) O#0 OO (d) Find the two critical values at the 0.10 level of significance. (Round to two or more decimal places.) | and || (e) Can you conclude that the independent variable is needed in the regression model? Yes No 미The least-squares regression equation is y=784.6x+12,431 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7962. In a particular region, 26.5 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $29,889. Is this income higher or lower than what you would expect? Why?
- 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…For x={1 2 3 4 5} and y={2 1 4 3 6} use normal equation (c =(ATA)-1ATy) to find with: a-) linear regression coefficients, b-) the linear regression equation, c-) residel sum of squares(RSS)The following is the result of the multiple linear regression analysis in STATISTICA, where the response Y = lung capacity of a person, xage = age of the person in years, xheight = height of the person in inches, = a categorical variable with 2 levels (0 = non- X smoke smoker, 1 = smoker), and xCaesarean = a categorical variable with 2 levels (0 = normal delivery, 1 = %3D %3D Caesarean-section delivery). b* Std.Err. Std.Err. t(720) p-value N=725 Intercept Age Height Smoke Caesarean of b 0.467772 0.017626 of b* -11.8001 0.1372 0.2790 -0.6407 -25.2263 7.7846 28.6552 -5.0142 0.000000 0.000000 0.000000 0.206427 0.026517 0.026340 0.754765 -0.074205 -0.033054 0.009735 0. 127774 0.092146 0.000001 0.022851 0.014799 0.014492 -0.2102 -2.2808 What is the predicted lung capacity of an 14-year old non-smoker whose height is 71 inches born by normal delivery? (final answer to 4 decimal places)
- Using 25 observations on each variable, a computer program generated the following multiple regression model: yhat=69.2+2.87x1+5.81x21.83x3 If the standard errors of the coefficients of the independent variables are, respectively, 1.34, 4.84, and 0.70, can you conclude that the independent variable x1 is needed in the regression model? Let β1, β2, and β3 denote the coefficients of the 3 variables in this model, and use a two-sided hypothesis test and significance level of 0.05 to determine your answer. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least two decimal places.) The two critical values at the 0.05 level of significance:(Round to at least two decimal places.) and Can you…The table contains data on vehicle speed (h) and fuel consumption (lt / 100km) of 5 randomly selected vehicles. Estimate the average fuel consumption of a vehicle traveling at 45 km / h using the simple linear regression equation between vehicle speed and fuel consumption. Speed 55 60 65 70 75 Consumption 13 12 11 10 9 a. 15 b. 8 c. 7 d. 20A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using two independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. With this regression model, the predicted price of a 10-year old home with 2,500 square feet of living area is __________. $205.00 $200,000.00 $205,000.00 $255,000.00
- The least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. Predict the median income of a region in which 30% of adults 25 years and older have at least a bachelor's degree.4. Consider a multiple linear regression model with two independent variables with 12 values in each variable. The coefficient of determination is obtained as 0.58. Evaluate the adjusted coefficient of detemination. for f nding Tote1 Cam ltinle lincorThe 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 = 83.5+ 2.21x₁ + 1.80x₂. The computer solution, based on a sample of eight weeks, provided SST = 25.4 and SSR = 23.495. (a) Compute and interpret R² and R2. (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 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 R2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis ---Select--- preferred since both R² and R2 show ---Select--- ✓percentage of the variability of y explained when both independent variables are used. . Adjusting for the number of…
