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It is required to use the data given in the table to estimate the parameters of the multiple linear regression equation by any of the estimation methods:
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- The y-intercept in a linear regression model is always relevant and of interest to investigators for every model constructed. True FalseQ5/ Use Linear Regression to fit the following data: X 1 2 4 5 6 Y 4 10 10 9 3Researchers at a large nutrition and weight management company are trying to build a model to predict a person’s body fat percentage from an array of variables. A variables selection method is used to build a regression model. SAS output for the final model is given in photo. Question: What percentage of the variation in percent body fat remains unexplained, even after introducing weight and abdomen circumference into the model, and then also determine the interpretation of the slope for weight?
- 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…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…The accompanying table shows results from regressions performed on data from a random sample of 21 cars. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). The equation CITY - 3.17 +0.823HWY was previously determined to be the best for predicting city fuel consumption. A car weighs 2700 lb, it has an engine displacement of 1.6 L, and its highway fuel consumption is 35 mi/gal. What is the best predicted value of the city fuel consumption? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate? Click the icon to view the table of regression equations. The best predicted value of the city fuel consumption is (Type an integer or a decimal. Do not round.). Regression Table I R² Adjusted R2 WT/DISP WT/HWY Predictor (x) Variables P-Value WT/DISP/HWY 0.000 0.942 0.000 0.748 0.000 0.942 0.000…
- The table shows the number of goals allowed and the total points earned (2 polnts for a win, and 1 point for an overtme or shootout loss) by 14 lce hockey teams over the course of a season The equation of the regression line is (a) Find the coefficient of determination,, and interpret the result (b) Find the standard error of the estimate, and interpret the resut Goals Allowed, x Points, y -0.560x 218.067 Use he data to answer the folowing questions 217 213 221 229 260 262 277 205 216 20s 217 208 257 246 66 70 105 105 0 83 47106 103 97 9182 91 88 Inco (a) r-O (Round to three decimal places as noeded.)The accompanying scatterplot shows the relationship between the age of an internet user and the amount of time spent browsing the internet per week (in minutes). The accompanying residual plot is also shown along with the QQ plot of the residuals. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. A.The residual plot displays a fan shape; therefore the Normality condition is not satisfied.B.The QQ plot mostly follows a straight line; therefore the Normality condition is satisfied.C.The scatterplot shows a negative trend; therefore the Normality condition is satisfied.D.The residual plot shows no trend; therefore the Normality condition is not satisfied.When using population size as the explanatory variable, x, and broadband subscribers as the response variable, y, for data on the number of individuals in a country with broadband access and the population size for 36 nations, the regression equation is y = 4,975,098 +0.0342x. a. Interpret the slope of the regression equation. Is the association positive or negative? Explain what this means. b. Predict broadband subscribers at the (i) population size 7,014,655, (ii) population size 1,155,173,053. c. For one nation, y = 71,110,000, and x = 322,413,902. Find the predicted broadband use and the residual for this nation. Interpret the value of this residual. a. Since the association is positive, the slope means that as the (Type an integer or a decimal.) b. (i) The predicted broadband subscribers for population size 7,014,655 is (Round to the nearest whole number as needed.) population size increases by 1 unit, the number of broadband subscribers tends to increase by 0.0342.
- The table lists the average monthly cost to workers for family health insurance for various years. Year, x Average Monthly Cost to Workers for Family Health Insurance $298 a) Use a graphing calculator to fit a regression line to the data. b) Predict the average monthly cost to workers for family health insurance in 2020, and compare the value with $493.3, which is obtained using the points (1,340) and (4,386). c) Find the correlation coefficient for the regression line, and determine whether the line fits the data closely. 2009, 0 2010, 1 2011, 2 340 348 2012, 3 367 2013, 4 2014, 5 386 406 a) The linear equation of the regression line that best models the data is y =x+. (Round to the nearest hundredth as needed.) b) The average monthly cost to workers for family health insurance in 2020 is predicted to be $ (Round to the nearest cent as needed.) Compare the above obtained value with $493.3 This value is $ $493.3 c) The correlation coefficient is (Round to the nearest thousandth as…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 = 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…
