uestion 2 (24 marks) Data was collected from 10 cities on the annual Auto Sales,
ID: 3054614 • Letter: U
Question
uestion 2 (24 marks) Data was collected from 10 cities on the annual Auto Sales, the average annual Household Income and the Population for each city. The data in the table below is shown in units of millions of dollars for Auto Sales, thousands of dollars for Household Income and millions for Population. City Auto Sales Household Income Population 3 4 5 10 18586 97100 527 40378 188 329 91 706578 90 124 11072 92 10288 1331106850 28929961111249 102 a) Determine the regression equation to predict 'Auto Sales' based on both the "Household Income" and 'Population'. Answer parts b) to d) based on this equation. Use all variables (see for follow-up) b) Is the overall regression significant at the 0.05 level of significance? How do you know? c) Describe the strength of the relationships between all pairings of variables. Are any of them significant (explain why/why not)? d) Based on your regression equation determine the point estimate and the 95% confidence interval for 'Auto Sales, (in million $'s) for a city with average ?0usehold income, of $75,000 and 'Population' of 90,000,000 e) Based on the regression equation what percentage of the variation in the variable 'Auto Sales' is explained by the regression? Based on your assessment of all the data provided by Minitab, refine / make any changes to the regression equation in part a) and show the regression equation you would recommend. You must provide reason(s) for your answer as taught in this course f)Explanation / Answer
We use Minitab to solve this question-
Minitab-
Regression Analysis: Auto Sales versus Household Income, Population
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 2 212199 106100 58.88 0.000
Household Income 1 9773 9773 5.42 0.053
Population 1 38093 38093 21.14 0.002
Error 7 12613 1802
Total 9 224812
Model Summary
S R-sq R-sq(adj) R-sq(pred)
42.4483 94.39% 92.79% 86.65%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -213.3 85.4 -2.50 0.041
Household Income 2.88 1.24 2.33 0.053 2.70
Population 1.123 0.244 4.60 0.002 2.70
Regression Equation
Auto Sales = -213.3 + 2.88 Household Income + 1.123 * Population
Prediction for Auto Sales
Regression Equation
Auto Sales = -213.3 + 2.88 Household Income + 1.123 Population
Variable Setting
Household Income 75
Population 90
Fit SE Fit 95% CI 95% PI
103.586 17.0998 (63.1513, 144.021) (-4.62664, 211.798)
________________________________________________________________________________________________
a)
Predicted regression equation-
Auto Sales^ = -213.3 + 2.88 Household Income + 1.123 Population
b)
From Analysis of variance-
At 0.05 significance level,
F =58.88 & it's corresponding p-value = 0.000 < 0.05 Which indicate significance of Regression.
c)
Strength and Relationship between variables Term and Household income is 2.88 which indicate positive relation between them also it's corresponding P-value = 0.053 > 0.05 therefore it is not significant.
Strength and Relationship between variables Term and Population is 1.123 which indicate positive relation between them also it's corresponding P-value = 0.002 < 0.05 therefore it is significant.
d)
Based on the regression equation point estimate and 95% confidence interval for Auto Sales is,
95% CI 95% PI
(63.1513, 144.021) (-4.62664, 211.798)
e)
Based on the regression equation 94.39% of the variation in the variable Auto sales is explained by regression.
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