The district sales manager for a major automobile manufacturer is studying car sales.Specifically, he would like to determine what factors affect the number of cars sold at adealership. To investigate, he randomly selects 12 dealers. From these dealers he obtainsthe number of cars sold last month, the minutes of radio advertising purchased last month,-the number of full-time salespeople employed in the dealership, and whether the dealer islocated in the city. The information is as follows:Cars SoldLast Month,Y127138159144139128Advertising,X₁181522231716SalesForce,X₂City,X₂10Yes15No14Yes12 Yes1212NoYesCars SoldLast Month,Y161180102163106149Advertising,X₂252615241825SalesForce,x₂141771610City,X3YesYesNoYesNoYesa. Develop a correlation matrix. Which independent variable has the strongest correla-tion with the dependent variable? Does it appear there will be any problems withmulticollinearity?b. Determine the regression equation. How many cars would you expect to be sold by adealership employing 20 salespeople, purchasing 15 minutes of advertising, and locatedin a city?c. Conduct a global test of hypothesis to determine whether any of the net regressioncoefficients differ from zero. Let a = .05.d. Conduct a test of hypothesis for the individual regression coefficients. Would youconsider deleting any of the independent variables? Let a = .05. Correlations: Cars sold, Advertising, Sales Force, CityCars sold Advertising Sales Force-0.6230.8720.639AdvertisingSales ForceCityCell Contents: Pearson correlationPredictorConstantCoef SE Coef53.25Advertising 0.65765.21115.771Regression Analysis: Cars sold versus Advertising, Sales Force, CityThe regression equation isCars sold 53.2 + 0.658 Advertising + 5.21 Sales Force + 15.8 City=Sales ForceCityS = 8.84607R-Sq 89.4%PT12.13 4.390.4467 1.470.0020.1791.148 4.54 0.0025.912 2.67 0.028DEAnalysis of VarianceSourceSSRegression3 5298.6Residual Error 8 626.0Total11 5924.70.5170.281SourceDE Seq SSAdvertising 1 2299.7Sales Force 12442.0City1556.9R-Sq (adj) - 85.5%MS1766.278.30.389F22.57P0.000

a) Here, cars sales at last month is the depending variable(Y) and advertising (X1) and sales force…

Answered: a. Develop a correlation matrix. Which…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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6.In simple linear regression, the sample correlation coefficient between the input variable and the output variable, and the estimated slope parameter : a.Must have the same sign (negative, zero, or positive) b.May have opposite signs c.Must have opposite signs d.Neither of the above
What does the correlation matrix for a multiple regression analysis contain?A. Multiple correlation coefficientsB. Simple correlation coefficientsC. Multiple coefficients of determinationD. Multiple standard errors of estimate
Consider a panel data set and the following regression model. Yit Bo + B₁Xit + ++ Uit What do subscripts / and t refer to? O A. Subscripts i and tidentify different time periods. O B. Subscripts / and t identify the entity and time period respectively. OC. Subscripts i and t identify different individuals. O D. Subscripts i and t identify the time period and entity respectively.
indlude answer(s) for part(s) A, B, C & D.
An economist wants to determine whether there is a linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. The data are shown in the table below. c. Compute and interpret the correlation coefficient. d. Compute and interpret the coefficient of determination. e. Test for the significance of the linear relationship. Use a 0.05 level of significance. State your conclusion. Hint: Your conclusion is either of the following. • There is a significant linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. • There is no significant linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. GDP 1.6 3.6 4.9 1.1 0.9 2.9 2.7 2.3 1.6 1.5 (trillion dollars) Carbon Dioxide Emissions 428.2 828.8 1214.2 444.6 264 415.3 571.8 454.9 358.7 573.5 (millions of metric tons)
Research was conducted on the amount of training for 5K and the time a contestant took to run the race. The researcher recorded the number of miles during training ( a 1 month period) and the time to complete the 5K. The results are below. Miles Trained 45 77 37 25 60 64 Time (Minutes) 32.9 28 36.2 27.5 19.5 18.3 a) Give the correlation coefficient. r = b) Give the equation of the regression line. Round the values to 4 deimal places.This is in the form y = ax + b, so the slope goes in the first box and the y-inercept in the 2nd box.y = x + c) Interpret the y-intercept (Explain it's meaning, do not just give its value.)d) Predict the time in the 5K if someone trained 37 miles.Use the rounded values entered for the slope and intercept of the regression line to compute the predicted y-value.y = e) Give the residual for 37 miles trained.This is the actual y value for the runner who trained for miles minus the predicted value.Residual=
9. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below. Calories, x Sodium, y 160 130 330 120 70 190 (a) x = 170 calories (c) x = 150 calories 180 (b) x = 80 calories 420 470 360 250 530 (d) x = 210 calories Find the regression equation. x+( (Round to three decimal places as needed.) y = Choose the correct graph below. OA. О В. OC. OD. 560- 560 560 560- 200 G 0IN T> 200 200 Calories Calories Calories Calories (a) Predict the value of y for x = 170. Choose the correct answer below. O A. 411.632 O B. 543.752 O C. 455.672 O D. not meaningful (b) Predict the value of y for x = 80. Choose the correct answer below. O A. 411.632 О В. 257.492 O C.…
GRC often rely heavily on raising money for an "annual fund" to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. In the studies described: O a. annual income is the predictor variable O b. the correlation between annual income and the size of the donation is negative. O c. the size of the donation to the annual fund is the predictor variable O d. All of the above O e. None of the above
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. a. Predict the sales next month for an employee with 2.5 years of experience. The predicted sales is 8.6 cars. b. Compute the coefficient of determination and interpret its meaning. The coefficient of determination is 0.234 Therefore, about _________% of the variation in monthly sales is explained by the years of sales experience. (Type an integer or decimal rounded to one decimal place as needed.)

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