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Regression Analysis - James McWhinney

PART ONE: Problem Statement: Mr. James McWhinney, president of Daniel-James Financial Services, believe there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousand) last month for each client sampled. [Please note: You may use Excel for all of your calculations, however, accurate interpretation for each part is required]

Number of Sales
Contacts, ($ thousands)
14 24
12 14
20 28
16 30
46 80
23 30
48 90
50 85
55 120
50 110

a) Let the sales amount be the response (dependent variable ), and the number of contacts be the exploratory (independent variable ). Create a scatter diagram, using Excel/MegaStat.

b) Determine the coefficient of correlation ( ). Determine the coefficient of determination ( ). What proportion of total variation in sales can be explained or accounted for, by the variation in number of contacts. Use .05

c) Can it be concluded that there is positive correlation between the number of contacts and sales? (Use )

Step 1: State the Null and Alternative Hypotheses, symbolically,
using the population coefficient of correlation ( -
Pronounced "rho")

Step 2: State the Decision Rule: Find the critical value of the test,
using Student's t-distribution ( Appendix F), and state the
rejection region.

Step 3: Compute the test statistic, and estimate the p-value.

Step 4: Make Decision regarding the Null Hypothesis.

Step 5: Interpret the results:

d) Determine the regression equation. Interpret the slope value.

e) Estimate the sales amount, if there were 48 contacts.

Solution Summary

The solution uses hypothesis testing and regression analysis to determine a regression equation for James McWhinney.