Complete parts (a) through (h) for the data below. X 4 5 6 8 9 О y 11 14 16 23 26 ииии 10 104 0- (f) Compute the sum of the squared residuals for the line found in part (b). 1 (Round to three decimal places as needed.) (g) Compute the sum of the squared residuals for the least-squares regression line found in part (d). (Round to three decimal places as needed.) С
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- For a sample of 15 rural counties in one state, a researcher has collected information about the rate of deaths due to traffic accidents per 1,000,000 population and the percentage of the population which consists of males, age 16 to 25. For these variables, find the least squares regression line and compute r and r squared. Write a sentence or two summarizing and explaining your results. RATE OF % OF POPULATION County Traffic Deaths Young Males County Traffic Deaths Young Males A 15 4 B 16 5 C 22 10 D 23 9 E 20 8 F 25 11 G 18 2 H 15 6 I 19 12 J 10 3 K 9 2 L 18 15 M 15 9 N 24 16 O 9 3while using the t-test to test whether regression is significant, in the model yi=β0+β1xi+εiyi=β0+β1xi+εi, what is the calculated student-t statistics (H0:β1=0H0:β1=0 versus H1:β1≠0H1:β1≠0). Calculate the least squares estimates of β0β0 in the model yi=β0+β1xi+εi Calculate the sum of squares of y denoted by Syy , the sum of squares of x denoted by Sxx and sum of squares (products) of x and y denoted by Sxy while using analysis of variance (ANOVA) to test whether regression is significant, in the model yi=β0+β1xi+εiyi=β0+β1xi+εi, what is the residual or error sum of squares due to regression, SSE. kindly help with this questionAdvertising 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%)
- 2. A company that holds the DVD distribution rights to movies previously released only in theaters wants to estimate sales revenue of DVDs based on box office success. The box office gross (in Php millions) for each of 22 movies in the year that they were released and the DVD revenue (in Php millions) in the following year are shown below and stored in (pic) a. construct a scatter plot. b. assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1.For a sample of 15 trees, the volume of lumber (y) (in cubic meters) and the diameter (x) (in centimeters) at a fixed height above ground level was measured. The following summary statistics were obtained: x̄ = 35.2 sx = 8.9 ȳ = 0.78 sy = 0.48 r = 0.95 a) Compute the least-squares regression line for predicting volume from diameter. B)Predict the volume for a tree whose diameter is 42 centimetersA study of IT companies has found the following data on the age of each company and its annual volume of sales: Age (years) Sales (000) 2 22 2.5 34 3 33 4 37 4.5 40 4.5 45 5 49 3 30 6 58 6.5 58 (a) Determine the least squares regression that relates the age of company variable to the sales variable in the form y = a + bx. (b) Provide a practical interpretation of the coefficients a and b. (c) Determine the ‘goodness of fit’ (R2) of the estimated regression line. d) Using the estimated regression line determined in (a), calculate what volume of sales would be predicted for a company that is 3.5 years of age. (e) If it was found that…
- 6/15 For the data set below: determine The least squares regression line. Round to two decimal places as needed. Compute the sum of the squares residuals for theyears Xi bonus Yi XiYi Xi2 4 5.7 22.8 16 2 3.5 7 4 7.4 10.1 74.74 54.76 5 9 45 25 2 2.7 5.4 4 12 12 144 144 Question 24 Are years of service and annual bonuses related? The annual bonuses of 6 randomly selected employees (measured in “thousands of dollars”) along their their respective years of service for the company. Suppose we estimate a linear regression using the Ordinary Least Squares technique of the form: Bonusi = b0 + b1(yearsi) where the subscript i indicates the ith employee The data is reproduced above for this experiment. Please calculate the standard error of the estimate, or s, for the regressionyears Xi bonus Yi XiYi Xi2 4 5.7 22.8 16 2 3.5 7 4 7.4 10.1 74.74 54.76 5 9 45 25 2 2.7 5.4 4 12 12 144 144 Question 25 Are years of service and annual bonuses related? The annual bonuses of 6 randomly selected employees (measured in “thousands of dollars”) along their their respective years of service for the company. Suppose we estimate a linear regression using the Ordinary Least Squares technique of the form: Bonusi = b0 + b1(yearsi) where the subscript i indicates the ith employee Using your excel output from this regression, what is the correct decision using the p value method for the slope test (assume an alpha level of .05) H0: B1 = 0 (not a linear relationship) H1: B1 ≠ 0 (is a linear relationship) a) a. fail to reject the null hypothesis, there is insufficient evidence of a linear relationship b) b. fail to reject the null hypothesis, there is sufficient evidence of…
- A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown. Term Coef (SE) Coef T-Value P-Value Constant 105.08 6.00 17.51 0.000 Foot length 2.599 0.238 10.92 0.000 S=5.90181 R–sq=65.42% (a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm. (b) The standard deviation of the residuals is s=5.9. Interpret the value in context. (c) The following histogram summarizes the 65 residuals. Assume that the distribution of residuals is approximately normal with mean 0cm and standard deviation 5.9cm. What percent of the residuals are greater than 8cm? Justify your answer.…A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown. Term Coef (SE) Coef T-Value P-Value Constant 105.08 6.00 17.51 0.000 Foot length 2.599 0.238 10.92 0.000 S=5.90181 R–sq=65.42% (a) The following histogram summarizes the 65 residuals. Assume that the distribution of residuals is approximately normal with mean 0cm and standard deviation 5.9cm. What percent of the residuals are greater than 8cm? Justify your answer. (b) Based on your answer to part (a), would it be surprising to randomly select a high school senior from the high school with a foot length of 20cm and a height greater than 165cm? Justify your answer.A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown. Term Coef (SE)Coef T-Value P-Value Constant 105.08 6.00 17.51 0.000 Foot length 2.599 0.238 10.92 0.000 S=5.90181 R–sq=65.42% (a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm.
