MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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i need Part 5,6,7 Solution just 

Exercise 2. In order to study the relationship of advertising and capital investment with corporate profits, the following data, recorded in units of $ 100, 000, were collected for 10 medium-sized firms in the same year. The variable y represents profit for the year, ri represents capilal investment, and rz represents advertising expenditures: Year y Capital ri Advertising ra 15 25 16 1 2 6 3 30 1 12 29 1 20 16 12 18 15 13 6 16 2 Using the model y = Bo +B11 +Br2+e and Minitab, find the least-squares prediction equation 1. for these data. 2. Give appropriate interpretations for the estimated coeflicients by, b1, b2. 3. Use the overall F test with Minitab to determine whether the model contributes significant information for the prediction of y. Use a = 0.05. Does advertising expenditure contribute significant information for the prediction of y, given that the capital r, is already in the model? Use a = 0.05 and Minitab output. 5. Construct a confidence interval for the mean value of the profit y, in a given year, for a capital investment z = 22 and a value of the advertising expenditures z2 = 6. Use a = 0.05. 6. Construct a prediction interval for the value of the profit y, in a given year, for a capital investment n = 22 and a value of the advertising expenditures r2 = 6. Use a = 0.05. Compare the confidence and the prediction intervals in term of size and precision. 7. Find the coefficient of determination, R and the adjusted R. Which of these two quantities is the most appropriate to find what percentage of the overall variation is explained by the model. Explain your choice! 8. Using Minitab, plot the residuals against the values of the capital investment ri and against the values of the advertising expenditures and finally against the predicted values y of the profit. Use these plots to analyze the equal variances assumptions. 9. Using Minitab, plot the normal plot of residuals. Do you observe a departure from the normality assumption?
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Transcribed Image Text:Exercise 2. In order to study the relationship of advertising and capital investment with corporate profits, the following data, recorded in units of $ 100, 000, were collected for 10 medium-sized firms in the same year. The variable y represents profit for the year, ri represents capilal investment, and rz represents advertising expenditures: Year y Capital ri Advertising ra 15 25 16 1 2 6 3 30 1 12 29 1 20 16 12 18 15 13 6 16 2 Using the model y = Bo +B11 +Br2+e and Minitab, find the least-squares prediction equation 1. for these data. 2. Give appropriate interpretations for the estimated coeflicients by, b1, b2. 3. Use the overall F test with Minitab to determine whether the model contributes significant information for the prediction of y. Use a = 0.05. Does advertising expenditure contribute significant information for the prediction of y, given that the capital r, is already in the model? Use a = 0.05 and Minitab output. 5. Construct a confidence interval for the mean value of the profit y, in a given year, for a capital investment z = 22 and a value of the advertising expenditures z2 = 6. Use a = 0.05. 6. Construct a prediction interval for the value of the profit y, in a given year, for a capital investment n = 22 and a value of the advertising expenditures r2 = 6. Use a = 0.05. Compare the confidence and the prediction intervals in term of size and precision. 7. Find the coefficient of determination, R and the adjusted R. Which of these two quantities is the most appropriate to find what percentage of the overall variation is explained by the model. Explain your choice! 8. Using Minitab, plot the residuals against the values of the capital investment ri and against the values of the advertising expenditures and finally against the predicted values y of the profit. Use these plots to analyze the equal variances assumptions. 9. Using Minitab, plot the normal plot of residuals. Do you observe a departure from the normality assumption?
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