Compute the least squares regression line
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Advertising share x and market share y fir a particular brand of cigarettes were sampled at ten randomly selected year. Summary information is:
n = 10, Ex = .688, Ex2 = .050072, Ey =.835, Ey2 = 0.079491, Exy = .060861
a) Compute the least squares regression line
b) Find the coefficient of determination r2 and explain what it means in the context of this problem.
c) Compute a 90% prediction interval for market share when advertising share is .07(7%)
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- A study was conducted to determine whether the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance. The verbal scores and final grades for all 1010 students in the class are shown in the table below. Find the following: (a) The correlation coefficient: ?= (b) The least squares line. NOTE:[for negitive ?1β1, for example ?1β1 = -2.4 write in form ?0+(−2.4)?β0+(−2.4)x ]:?̂ = Calculate the residual for the sixth studentSolve the second question in regression analysisAdd to MyRegistry 9 Mail - sgorham@a.. Like father, like son: In 1906, the statistician Karl Pearson measured the heights of 1078 pairs of fathers and sons. The following table presents a sample of 6 pairs, with height measured in inches, simulated from the distribution specified by Pearson. Compute the least-squares regression line for predicting son's height (v) from father's height (x). Round the slope and y-intercept values to at least four decimal places. Father's Son's height height 73.6 74.9 66.7 68.8 70.1 73.3 72.3 71.9 73.6 76.5 69.3 71.4 Send data to Excel Regression line equation: Save For Later Submit Assignment Check Answer © 2021 McGraw Hill LLC. AlI Rights Reserved. Terms of Use Privacy Center
- The calories and sugar content per serving size of ten brands of breakfast cereal are fitted with a least squares regression line with computer outputs:The following data represent the speed at which a ball was hit (in miles per hour) and the distance it traveled (in feet) for a random sample of home runs in a Major League baseball game in 2018. Complete parts (a) through (f). Click here to view the data. Click here to view the critical values of the corelation coefficient (a) Find the least-squares regression line treating speed at which the ball was hit as the explanatory variable and distance the ball traveled as the response variable. y (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. Begin by interpreting the slope. Data table O A. The slope of this least-squares regression line says that the distance the ball travels increases by the slope with every 1 mile per hour increase in the speed that the ball was hit. O B. The slope of this least-squares regression line shows the increase in the speed that the ball was hit with every 1 foot increase in the distance that the ball was…Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. Thecorrelation coefficient is 0.944 and the least squares regression line is y = 0.199x + 11.982. Complete parts (a) and (b)below.Height, x27.5 25.5 26.25 25.25 27.5 26.25 26 27.25 27.25 27 27.25 ФHead Circumference, # 17.5 17.0 17.2 17.0 17.5 17.3 17.2 17.4 17.3 17.3 17.4(a) Compute the coefficient of determination, R?R?.% (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 inis explained by the least-squares regression model.According to the residual plot, the linear model appears to be (Round to one decimal place as needed.)
- An article on the cost of housing in California that appeared in the San Luis Obispo Tribunet included the following statement: "In Northern California, people from the San Francisco Bay area pushed into the Central Valley, benefiting from home prices that dropped on average $4000 for every mile traveled east of the Bay area." If this statement is correct, what is the slope of the least-squares regression line, ý = a + bx, where y = house price (in dollars) and x = distance east of the Bay (in miles)? Your answer cannot be understood or graded. More Information3. The following figure shows the Excel output of a least square multiple linear regression for the scores in a test (variable Y) with Hours (X1, the number of hours spent reviewing) and Prep Exam (X2, the number of exams to take) as independent variables. SUMMARY OUTPUT Regression Statisties Multiple R R Square Adjusted R Square 0.857 0.734 0.703 Standard Error 5.366 Observations 20 ANOVA df Significance F 23.46 MS Regression 1350.76 675.38 0.00 Residual 17 489.44 28.79 Total 19 1840.20 Coefficients Standord Error tStat Pvalue 67.67 Lower 95N Upper 95N Intercept 2.82 24.03 0.00 61.73 73.61 hours 5.56 0.90 6,18 0.00 3.66 7.45 prep exams -0.60 0.91 0.66 052 -2.53 133 a. What is the value of r? What is the practical meaning of this value? b. What is the coefficient of Hours? Interpret this value. c. What is the coefficient of Prep Exam? Interpret this value.The output table below represents the results of the estimation of household expenditures (Y) and income (X) in thousand dollars. Considering the output table below, answer the following questions. Dependent Variable: Y Method: Least Squares Date: 12/28/16 Time: 15:29 Sample: 2000 2010 Included observations: 11 Variable Coefficient Std. Error t-Statistic Prob. C 0.229334 2.938536 0.078044 0.9395 X 0.354833 0.024783 14.31783 0.0000 R-squared 0.957944 Mean dependent var 37.45455 Adjusted R-squared 0.953271 S.D. dependent var 21.01125 S.E. of regression 4.541976 Akaike info criterion 6.027567 Sum squared resid 185.6659 Schwarz criterion 6.099911 Log likelihood -31.15162 Hannan-Quinn criter. 5.981964…
- The output table below represents the results of the estimation of household expenditures (Y) and income (X) in thousand dollars. Considering the output table below, answer the following questions. Dependent Variable: Y Method: Least Squares Date: 12/28/16 Time: 15:29 Sample: 2000 2010 Included observations: 11 Variable Coefficient Std. Error t-Statistic Prob. C 0.229334 2.938536 0.078044 0.9395 X 0.354833 0.024783 14.31783 0.0000 R-squared 0.957944 Mean dependent var 37.45455 Adjusted R-squared 0.953271 S.D. dependent var 21.01125 S.E. of regression 4.541976 Akaike info criterion 6.027567 Sum squared resid 185.6659 Schwarz criterion 6.099911 Log likelihood -31.15162 Hannan-Quinn criter. 5.981964…The following data represent the speed at which a ball was hit (in miles per hour) and the distance it traveled (in feet) for a random sample of home runs in a Major League baseball game in 2018. Complete parts (a) through (f). Click here to view the data. Click here to view the critical values of the correlation coefficient. (a) Find the least-squares regression line treating speed at which the ball was hit as the explanatory variable and distance the ball traveled as the response variable. y = 5x+ (5 (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. Begin by interpreting the slope. A. The slope of this least-squares regression line says that the distance the ball travels increases by the slope with every 1 mile per hour increase in the speed that the ball was hit. O B. The slope of this least-squares regression line shows the increase in the speed that the ball was hit with every 1 foot increase in the distance that the ball was hit.…An administrator wants to investigate the relationship between the numbers of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected. Distance to Work (miles) 2 4 6 6 9 8 10 12 12 15 Number of Days Absent 8 5 8 6 6 4 6 3 5 3 Develop the least square regression line to predict the number of days absent based on the distance to work. Enter the regression coefficients in xx.xxx format. Round the value to three decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the coefficient is negative. Do not include plus sign in your response. For example, if the coefficient is +6.1563 then enter 06.156 as your answer, if the coefficient is -0.54765 then enter -00.548 and if the answer is -1.6435 then enter -01.644 Ŷ=b0+b1X Constant/intercept…
