An online clothing company is keeping track of their customers purchases. Company also offers a credit card where customers get additional offers if they use that card when they make purchases from their online store. For those customers who has their credit card, the company has additional information such as age, yearly income, etc. The company management is interested in looking at the relationship between the income (in 1000s of dollars) and the total yearly purchases from their store for these credit card holders . They have gathered this information from a random sample of 42 credit card holders. Below provided is a partial MINITAB output for predicting the yearly purchases from the income. Identify the response and the predictor variable in this study.Write the equation of the least squares regression line for predicting the total yearly purchase from the income of the customer.What percentage of variation in total yearly purchase is explained by income of the customer?We want to test if the total yearly purchase increases with the income.Write the appropriate null and alternative hypothesis you would formulate to answer this question. Use the proper notations when setting up the H0 and H1. Calculate the test statistic.What is the degrees of freedom of distribution for the test statistic under the null hypothesis?Calculate the p value. You may use the table or MINITAB to find the final p value; however, you need to write the probability statement for the p value for this test. Write the final conclusion in the context of the problem. Use 5% significance level. Find the sample correlation between the income and the yearly purchase.Suppose that your annual salary is $55,000 (i.e.: 55 in $1000). Assuming you are a new customer who applied for the credit card, the company would like to get an interval estimation for total yearly purchase by you using the fitted regression model . Which one of below would be the appropriate interval estimation. Explain the reason for your choice.Confidence interval for mean response when income is 55.Prediction interval for an individual observation when income is 55. CoefficientsTermCoef SE CoefT-ValueP-ValueVIFConstant3.717.880.470.640Income11.3590.1481.00Model SummaryS R-sq R-sq(adj)14.018799.33%99.31%R-sq(pred)99.25%Analysis of VarianceSourceDFAdj ssAdj MSF-Value P-ValueRegression1116302211630225917.940.000Income1 116302211630225917.940.000Error407861197Total41 1170883

The objective of this question is to understand the relationship between the income of the customers…

Answered: Coefficients Term Coef SE Coef T-Value…

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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Question

An online clothing company is keeping track of their customers purchases. Company also offers a credit card where customers get additional offers if they use that card when they make purchases from their online store. For those customers who has their credit card, the company has additional information such as age, yearly income, etc. The company management is interested in looking at the relationship between the income (in 1000s of dollars) and the total yearly purchases from their store for these credit card holders . They have gathered this information from a random sample of 42 credit card holders. Below provided is a partial MINITAB output for predicting the yearly purchases from the income.

Identify the response and the predictor variable in this study.
Write the equation of the least squares regression line for predicting the total yearly purchase from the income of the customer.
What percentage of variation in total yearly purchase is explained by income of the customer?
We want to test if the total yearly purchase increases with the income.
- Write the appropriate null and alternative hypothesis you would formulate to answer this question. Use the proper notations when setting up the H0 and H1.
- Calculate the test statistic.
- What is the degrees of freedom of distribution for the test statistic under the null hypothesis?
- Calculate the p value. You may use the table or MINITAB to find the final p value; however, you need to write the probability statement for the p value for this test.
- Write the final conclusion in the context of the problem. Use 5% significance level.
Find the sample correlation between the income and the yearly purchase.
Suppose that your annual salary is $55,000 (i.e.: 55 in $1000). Assuming you are a new customer who applied for the credit card, the company would like to get an interval estimation for total yearly purchase by you using the fitted regression model . Which one of below would be the appropriate interval estimation. Explain the reason for your choice.
- Confidence interval for mean response when income is 55.
- Prediction interval for an individual observation when income is 55.

Coefficients
Term
Coef SE Coef
T-Value
P-Value
VIF
Constant
3.71
7.88
0.47
0.640
Income
11.359
0.148
1.00
Model Summary
S R-sq R-sq(adj)
14.0187
99.33%
99.31%
R-sq(pred)
99.25%
Analysis of Variance
Source
DF
Adj ss
Adj MS
F-Value P-Value
Regression
1
1163022
1163022
5917.94
0.000
Income
1 1163022
1163022
5917.94
0.000
Error
40
7861
197
Total
41 1170883

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