i. Specify the regression model.ii.Interpret the result of the estimated coefficients of this model.III.What is the coefficient of determination? What does this statistic tell you? Tutorial 8: Multiple RegressionThe table below reports the results of the regression analysis on the relationships betweensalary data for n=14 randomly sampled systems analysts from a large population of suchindividuals and their years of experience (Exper) and years of postsecondary education(Educ):VariableCoefficientsStandard ErrorI-statp-valueInterceptEXPER2690204.64551116.920.000825.74.040.002EDUC1603.7536.32.990.012s= 2156R-sq = 0.672R-sq (Adj) = 0.613ANOVASourceDFSSMSF-statP0.002RegressionResidualTotal21048621685243108411.281151149976464999813156012144Prediction Interval3Salary45Predicted value564676.7Prediction Interval (95%)8Lower limit515489Upper limit6138610Interval Estimate of Expected Value (95%)Lower limit11125518013Upper limit57755

a) Here, y=salary, x1=years of experience, x2=years of postsecondary education. From the output, the…

Answered: i. Specify the regression model. ii.…

i. Specify the regression model. ii. Interpret the result of the estimated coefficients of this model. iii. What is the coefficient of determination? W hat does this statistic tell you?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
The owner of a new pizzeria in town wants to study the relationship between weekly revenue and advertising expenditures. All measures are recorded in thousands of dollars. The summary output for the regression model is given below. ANOVA dfdf SSSS MSMS FF Significance FF Regression 11 19.5214756219.52147562 19.5214756219.52147562 19.0348674019.03486740 0.0024032820.002403282 Residual 88 8.2045123678.204512367 1.025564051.02556405 Total 99 27.7259879927.72598799 Step 2 of 3 : What is the adjusted coefficient of determination for this model, R2aRa2? Round your answer to four decimal places.
A Simple Linear Regression (SLR) was performed where the monthly Revenue ("Rev", the y-variable) was regressed on the monthly Advertising Expenditures ("Expend", the x-variable). The Excel-generated Regression output is provided below: ANOVA df SS MS F Significance F Regression 1 492.528125 492.528125 10.65525634 0.046980871 Residual 3 138.671875 46.22395833 Total 4 631.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 23.1328125 5.324310936 4.344752359 0.022510469 6.188478833 40.07714617 Expend 3.1015625 0.950164031 3.264239014 0.046980871 0.077716489 6.125408511 a. From the Excel-generated Regression output above, give the value of b0, the estimated y-intercept. Round off your answer to the fourth decimal place. b0 =____. b. From the Excel-generated Regression output above, give the value of b1 , the estimated slope. Round off your answer to the fourth decimal place. b1 = _________
A Simple Linear Regression (SLR) was performed where the monthly Revenue ("Rev", the y-variable) was regressed on the monthly Advertising Expenditures ("Expend", the x-variable). The Excel-generated Regression output is provided below: ANOVA df SS MS F Significance F Regression 1 492.528125 492.528125 10.65525634 0.046980871 Residual 3 138.671875 46.22395833 Total 4 631.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 23.1328125 5.324310936 4.344752359 0.022510469 6.188478833 40.07714617 Expend 3.1015625 0.950164031 3.264239014 0.046980871 0.077716489 6.125408511 a. From the Excel-generated Regression output above, give the value of b subscript o, the estimated y-intercept. Round off your answer to the fourth decimal place. b subscript 0 = Blank 1. Fill in the blank, read surrounding text. b. From the Excel-generated Regression output above, give the value of b subscript 1, the estimated slope. Round off your answer to…
A car dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on theemployee's number of years of sales experience. The accompanying regression output was developed based on a random sample of employees. ANOVA df SS Regression 1 79.909407 Residual 23 261.210593 Total 24 341.12 Coefficients Standard Error Intercept 7.271539 1.229763 Slope 0.539854 1. Predict the sales next month for an employee with 2.5 years of experience. The predicted sales is 8.6 cars. 2. Compute the coefficient of determination and interpret its meaning. The coefficient of determination is 0.234. 3. Do the sample data provide evidence that the model is useful for predicting average monthly sales for employees based on their sales experience using α=0.05? The test statistic is (Type an integer or decimal rounded to two decimal places as…
A car dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on theemployee's number of years of sales experience. The accompanying regression output was developed based on a random sample of employees. ANOVA df SS Regression 1 79.909407 Residual 23 261.210593 Total 24 341.12 Coefficients Standard Error Intercept 7.271539 1.229763 Slope 0.539854 0.203521 The coefficient of determination is 0.234 Test statistic= 0.704 P-value= 0.014 Construct a 95% confidence interval around the sample slope and interpret its meaning. The confidence interval is (__________,_________). (Type an integer or decimal rounded to three decimal places as needed.)
Multiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin (1971), the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple regression model was constructed to predict the cash price of wheat using three supply-and-demand explanatory variables: economic growth, population growth, and meat consumption. Data for 24 years were used to construct the regression equation, and a prediction for the suspect period was computed from this equation. Which of the independent variables is the most significant predictor of the cash price of wheat? a. Intercept b. Economic Growth c. Population Growth d. Meat Consumption
Multiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin (1971), the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple regression model was constructed to predict the cash price of wheat using three supply-and-demand explanatory variables: economic growth, population growth, and meat consumption. Data for 24 years were used to construct the regression equation, and a prediction for the suspect period was computed from this equation Based on a significance level of 5%, which of the following independent variables significantly predict the cash price of wheat? a. Economic Growth b. Population Growth c. Meat Consumption d. All the independent variables significantly predict the cash price of wheat.
Multiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin (1971), the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple regression model was constructed to predict the cash price of wheat using three supply-and-demand explanatory variables: economic growth, population growth, and meat consumption. Data for 24 years were used to construct the regression equation, and a prediction for the suspect period was computed from this equation. The actual cash price of wheat under investigation in 1963 was $2.13. Based on the comparison of the correct predicted cash price calculated in the previous question and the actual cash price, what does the evidence suggest about Cargill, Inc.? a. Because the predicted price is relatively close to the actual price (within one cent), Cargill, Inc. probably did not artificially manipulate the price of wheat.…
Multiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin (1971), the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple regression model was constructed to predict the cash price of wheat using three supply-and-demand explanatory variables: economic growth, population growth, and meat consumption. Data for 24 years were used to construct the regression equation, and a prediction for the suspect period was computed from this equation. In 1963, during the period in question, economic growth was 3.8; population growth was 1.40; and meat consumption was 152.95. Based on these values, what would be the predicted cash price of wheat at this time in 1963?
Multiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin (1971), the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple regression model was constructed to predict the cash price of wheat using three supply-and-demand explanatory variables: economic growth, population growth, and meat consumption. Data for 24 years were used to construct the regression equation, and a prediction for the suspect period was computed from this equation. The following output represents the regression analysis. . Before the judge and jury consider the results of the regression model, they must ensure that the model is valid. What is the proper hypothesis test for this model, and what is the proper conclusion?
A car dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on theemployee's number of years of sales experience. The accompanying regression output was developed based on a random sample of employees. ANOVA df SS Regression 1 79.909407 Residual 23 261.210593 Total 24 341.12 Coefficients Standard Error Intercept 7.271539 1.229763 Slope 0.539854 0.203521 The predicted sales is 8.6 cars. The coefficient of determination is 0.234 Test Statistic is 7.04 P-value=