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) 99.33% 14.0187 99.31% Analysis of Variance R-sq(pred) 99.25% 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
Please note that this question consists of four parts. However you MUST show all the mathematical work/explanation to following questions. Just giving the answer without adequate work/explanation may result in zero for the 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.
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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?
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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.
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