The regional manager of a franchise business is interested in understanding how income in a region affects sales. Below is a regression output for sales ($’000) regressed on the average household income of an area ($’000) Linear Fit Sales = 14.5774 + 2.9048*Income Summary of Fit RSquare 0.9683 RSquare Adj 0.9630 Root Mean Square Error 3.1083 Mean of Response 43.6250 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 1 1771.9048 1771.90 183.3946 Error 6 57.9702 9.66 Pro>F C. Total 7 1829.8750 ItI Intercept 14.5774 2.4101 6.05 0.0009* Income 2.9098 0.2145 13.54 < 0.0001* Answer the following questions: (i) What is the average sales across all regions? (ii) Interpret the slope of regression (iii) What is the prediction of the value of sales in a region with an average household income of $30,000?
The regional manager of a franchise business is interested in understanding how income in a region affects sales. Below is a regression output for sales ($’000) regressed on the average household income of an area ($’000) Linear Fit Sales = 14.5774 + 2.9048*Income Summary of Fit RSquare 0.9683 RSquare Adj 0.9630 Root Mean Square Error 3.1083 Mean of Response 43.6250 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 1 1771.9048 1771.90 183.3946 Error 6 57.9702 9.66 Pro>F C. Total 7 1829.8750 ItI Intercept 14.5774 2.4101 6.05 0.0009* Income 2.9098 0.2145 13.54 < 0.0001* Answer the following questions: (i) What is the average sales across all regions? (ii) Interpret the slope of regression (iii) What is the prediction of the value of sales in a region with an average household income of $30,000?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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The regional manager of a franchise business is interested in understanding how income in a region affects sales. Below is a regression output for sales ($’000) regressed on the average household income of an area ($’000)
Linear Fit
Sales = 14.5774 + 2.9048*Income
Summary of Fit
RSquare 0.9683
RSquare Adj 0.9630
Root Mean Square Error 3.1083
Mean of Response 43.6250
Analysis of Variance
Source
DF
Sum of Squares
Mean Square
F Ratio
Model
1
1771.9048
1771.90
183.3946
Error
6
57.9702
9.66
Pro>F
C. Total
7
1829.8750
ItI
Intercept
14.5774
2.4101
6.05
0.0009*
Income
2.9098
0.2145
13.54
< 0.0001*
Answer the following questions:
(i) What is the average sales across all regions?
(ii) Interpret the slope of regression
(iii) What is the prediction of the value of sales in a region with an average household income of $30,000?
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