i need Part 1,2,3 Solution Exercise 2.In order to study the relationship of advertising and capital investment with corporateprofits, the following data, recorded in units of $ 100, 000, were collected for 10 medium-sized firms in the sameyear. The variable y represents profit for the year, ri represents capilal investment, and rz represents advertisingexpenditures:Year y Capital riAdvertising ra1525161263301122912016121815136162Using the model y = Bo +B11 +Br2+e and Minitab, find the least-squares prediction equation1.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 significantinformation for the prediction of y. Use a = 0.05.Does advertising expenditure contribute significant information for the prediction of y, given thatthe 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 capitalinvestment 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 investmentn = 22 and a value of the advertising expenditures r2 = 6. Use a = 0.05. Compare the confidence and theprediction intervals in term of size and precision.7.Find the coefficient of determination, R and the adjusted R. Which of these two quantitiesis the most appropriate to find what percentage of the overall variation is explained by the model. Explainyour choice!8.Using Minitab, plot the residuals against the values of the capital investment ri and against thevalues of the advertising expenditures and finally against the predicted values y of the profit. Use these plotsto analyze the equal variances assumptions.9.Using Minitab, plot the normal plot of residuals. Do you observe a departure from the normalityassumption?

Answers: 1. The prediction equation is: y = -8.18 + 0.292*x1 + 4.434*x2

1. Using the model y = Bo + B11+Br2+e and Minitab, find the least-squares prediction equation for these data. 2. Give appropriate interpretations for the estimated coeficients by, b1, ba. 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.

1. Using the model y = Bo + B11+Br2+e and Minitab, find the least-squares prediction equation for these data. 2. Give appropriate interpretations for the estimated coeficients by, b1, ba. 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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

i need Part 1,2,3 Solution

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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