Author:
Christine Farr

A business person in Georgia State is trying to estimate the relationship between the average weekly income in a county and the weekly expenditure on a certain staple Z. Data is collected in 6 counties and below is the tabulation:Average Income / Week Average Expenditure on Z$200 103.00$250 91.00$300 82.00$350 65.00$400 51.00$500 23.00A simple linear regression of a model EXPENDITURE = b + b INCOMEWas run and the computer output is shown below:INCOME & EXPENDITURE ON STAPLE ZREGRESSION FUNCTION & ANOVA FOR EXPEND[Z]EXPEND[Z] = 159.0714 - 0.269714 INCOMER-Squared = 0.994999Adjusted R-Squared = 0.993749Standard error of estimate = 2.309143Number of cases used = 6Analysis of Variance p-valueSource SS df MS F Value Sig ProbRegression 4243.50500 1 4243.50500 795.83480 0.000009Residual 21.32857 4 5.33214Total 4264.83300 5INCOME & EXPENDITURE ON STAPLE ZREGRESSION COEFFICIENTS FOR EXPEND[Z]Two-Sided p-valueVariable Coefficient Std Error t Value Sig ProbConstant 159.07140 3.32342 47.86370 0.000001INCOME -0.26971 0.00956 -28.21054 0.000009 *Standard error of estimate = 2.309143Durbin-Watson statistic = 1.687953QUESTIONS(a) What is the estimated equation for the model: EXPENDITURE = b + b INCOME(b) What kind of relationship exists between average income and average expenditure on staple Z? Does this relationship make sense to you? Why or why not?(c) What can you say about staple Z? Name an example of staple (good) that exhibits the behavior of Z.(d) Interpret the values of the b-coefficients (intercept and slope) in the estimated regression.(e) At a level of significance α = 0.01, test for the validity of the relationship. What is your conclusion?(f) Forecast the expected expenditure on staple Z for a household with average weekly income of (i) $100, (ii) $600. To come up with your forecasts what assumption(s) did you make?(2) REGRESSION ANALYSIS - ApplicationsA business person in Georgia State is trying to estimate the relationship between the average weekly income in a county and the weekly expenditure on a certain staple X. Data is collected in 6 counties and below is the tabulation:Average Income / Week Average Expenditure on X$150 $33$200 $39$250 $47.50$300 $55$400 $65.50$500 $72.50A simple linear regression of a model EXPENDITURE = b + b INCOMEWas run and the computer output is shown below:INCOME & EXPENTITURE ON STAPLE XREGRESSION FUNCTION & ANOVA FOR EXPEND[X]EXPEND[X] = 17.40686 + 0.115588 INCOMER-Squared = 0.977573Adjusted R-Squared = 0.971966Standard error of estimate = 2.552152Number of cases used = 6Analysis of Variancep-valueSource SS df MS F Value Sig ProbRegression 1135.65400 1 1135.65400 174.35450 0.000190Residual 26.05392 4 6.51348Total 1161.70800 5INCOME & EXPENTITURE ON STAPLE XREGRESSION COEFFICIENTS FOR EXPEND[X]Two-Sided p-valueVariable Coefficient Std Error t Value Sig ProbConstant 17.40686 2.82528 6.16111 0.003522INCOME 0.11559 0.00875 13.20434 0.000190 *QUESTIONS(a) What is the estimated equation for the model: EXPENDITURE = b + b INCOMEAnswer(b) What kind of relationship exists between average income and average expenditure on staple X? Does this relationship make sense to you? Why or why not?Answer(c) What can you say about staple X? Name an example that exhibits the behavior of staple XAnswer(d) Interpret the values of the b-coefficients (intercept and slope) in the estimated regression.Answer(e) At a level of significance α = 0.01, test for the validity of the relationship. What is your conclusion?Answer(f) Forecast the expected expenditure on staple X for a household with average weekly income of (i) $100, (ii) $600. To come up with your forecasts what assumption(s) did you make?Answer

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