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- Using a sample of 46 college students, we want to determine if there is a significant correlation between weight (in lbs.) and weekly exercise (in minutes). The results of a correlation and regression analysis are indicated in the Excel output below. The mean weight (the independent variable) was 166.80 lbs., and the mean weekly exercise time (the dependent variable) was 158.83 minutes. SUMMARY OUTPUT Regression Statistics Multiple R 0.027082077 R Square 0.000733439 Adjusted R Square -0.021977165 Standard Error 79.41761298 Observations 46 ANOVA df SS MS F Significance F Regression 1 203.6896 203.6896 0.032295 0.858207 Residual 44 277514.9 6307.157 Total 45 277718.6 Coefficients Standard Error t Stat P-value Lower 95%…o pis pe Suppose a doctor measures the height, x, and head circumference, y. of 11 children and obtains the data below. The correlation coefficient is 0.899 and the least squares regression line is y = 0.185x+ 12.276. Complete parts (a) and (b) below. Height, x Head Circumference, y 17.4 17.1 17.2 16.9 17.4 17.1 17.1 17.3 17.3 17.3 17.4 27.75 25.75 26.75 25.75 28 26.5 25.75 26.75 27 27.25 27.25 (a) Compute the coefficient of determination, R?. R2 = % (Round to one decimal place as needed) (b) Interpret the coefficient of determination k Approximately % of the variation in (Round to one decimal place as needed.) is explained by the least-squares regression model. Enter your answer in each of the answer boxes. Save for Later DUE RTTT:DY PIVT Score: o:5SYO Tor Tv attempts 3:35 PA- a 2/22/202 Type here to search insert prt sc 4+ backsp %23 6. 8.Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation coefficient is 0.866 and the least squares regression line is y = 0.143x + 13.465. Complete parts (a) and (b) below. Height, x Head Circumference, y 17.3 17.0 17.2 17.1 27.25 25 26.5 25 27.75 26.5 26 26.75 26.75 27 27 17.4 17.3 17.1 17.4 17.4 17.4 17.3 (a) Compute the coefficient of determination, R?. R2 = % (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. Approximately % of the variation in is explained by the least-squares regression model. (Round to one decimal place as needed.)
- 7) Below is a multiple regression in which the dependent variable is market value of houses and the independent variables are the age of the house and square footage of the house. The regression was estimated for 42 houses. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total df 2 39 41 0.745495 0.555762 0.532981 7211.848 42 SS 2537650171 2028419591 4566069762 Coefficients Standard Error MS 1.27E+09 52010759 F 24.39544 Significance F 1.3443E-07 Upper 95% t Stat P-value Lower 95% Intercept 47331.38 13884.34664 3.408974 0.001528 19247.6673 House Age -825.161 607.3128421 -1.35871 0.182046 -2053.5662 Square Feet 40.91107 6.696523994 6.109299 3.65E-07 27.3660835 7A. What is the estimated regression equation for determining the market value of houses? 7B. Discuss tests of significance of the regression 7C. What percentage of the variation in the dependent variable, Market Value, is explained by the regression…Fill in the blanks.a. Positive correlations between observations of the response variable result in an underestimate of_______b. Data collected from a designed experiment is generally preferable to data obtained from_______c. Adata point whose removal has a substantial effect on one or more sample regression coefficients is called an_______For an ANOVA test of significance of a regression model with 10 regressor variables and 50 observations, what is the degree of freedom of the SSr? choices 11 10 39 49
- Data on 12 randomly selected athletes was obtained concerning their cardiovascular fitness (measured by time to exhaustion running on a treadmill) and performance in a 20-km ski race. Both variables were measured in minutes and a regression analysis was performed. ski 85 2.5. treadmill = Coefficients Estimate (Intercept) Treadmill 85 - 2.5 Std. Error What is the test statistic? -2.5 0.45 1 Is there sufficient evidence to conclude that there is a linear relationship between cardiovascular fitness and ski race performance? Round your answers to three decimal places. Using your answer from the previous question, find the p-value. Part 2 oYou plan to fit a regression model that will be used to predict first-year college GPA (FYGPA) from high-school GPA (HSGPA), ACT score (ACT), first-generation status (Yes or No), socioeconomic class (lower class, lower to middle class, middle to upper class, and upper class), and school type (public or private). What is the total number of estimated regression coefficients? If the sample size is n = 250 students, what are the degrees of freedom for the following sources of variation: Regression Error TotalWe give the total variation, the unexplained variation (SSE), and the least squares point estimate b1 . Total variation = 13.459; SSE = 2.806; b1 = 2.6652 Click here for the Excel Data File Using the information given, find the explained variation, the simple coefficient of determination (r2), and the simple correlation coefficient (r). Interpret r2. (Round your answers to 3 decimal places. Round your percent to 1 decimal place.) Explained variation r2 r % of the variation in demand can be explained by variation in price differential.
- Fill in the blanks. a. Positive correlations between observations of the response variable result in an underestimate of ________. b. Data collected from a designed experiment is generally preferable to data obtained from ________. c. Adata point whose removal has a substantial effect on one or more sample regression coefficients is called an _________.Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. The correlation coefficient is 0.858 and the least squares regression line is y = 0.228x +11.187. Complete parts (a) and (b) below. Height, x 27.5 25.75 26.5 25.5 27.25 26.25 25.75 27.25 27 27.25 27 Head Circumference, y 17.4 17.2 17.2 16.9 17.6 17.1 17.1 17.4 17.4 17.3 17.3 (a) Compute the coefficient of determination, R². R² =% (Round to one decimal place as needed.) (b) Interpret the coefficient of determination and comment on the adequacy of the linear model. Approximately % of the variation in (Round to one decimal place as needed.) is explained by the least-squares regression model. According to the residual plot, the linear model appears to beUsing the sample data from the accompanying table, complete parts (a) and (b). E Click the icon to view the data table (a) Explain why it does not make sense to construct confidence or prediction intervals based on the least-squares regression equation. Choose the correct answer below. O A. It does not make sense to construct confidence or prediction intervals based on the least-squares regression equation because there is a linear relationship between sugar content and calories in high-protein and moderate protein energy bars. O B. It does not make sense to construct confidence or prediction intervals based on the least-squares regression equation because there is no linear relationship between sugar content and calories in high-protein and moderate protein energy bars. O C. It does not make sense to construct confidence or prediction intervals based on the least-squares regression equation because the residuals are not normally distributed. (b) Construct a 95% confidence interval for…