Homework SourseIn order to determine the appropriate stocking strategies fo
In order to determine the appropriate stocking strategies for wines, a liquor store would like to determine whether there is a relationship between rating of wines by an expert (on 1 to 5 scale) and the quantity (in cases) of that wine sold in a year. The data table follows:
Expert Rating
# of cases Purchased
The regression output generated by the owner follows.
What is the correlation between rating and purchases? What % of the variation is explained by out linear model?
What are your conclusions about the two types of hypotheses?
Based on the regression, predict the number of cases you could expect to be purchased is a wine has a rating of 2.5.
If asked to predict the number of cases you could expect to be purchased on a wine with a rating of 1.8, what would your response be?
Predict the cases purchased when a wine has a rating of 3.6, how does this compare to the actual purchases for a wine with this rating?
Based on residual plot do you go ahead with this linear model or should you consult some statistician who is more knowledgeable about assumptions?
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.7816
R Square
0.6108
Adjusted R Square
0.546
Standard Error
3.5426
Observations
8
ANOVA
Df
SS
MS
F
Significance F
Regression
1
118.198
118.198
9.418
0.022
Residual
6
75.301
12.550
Total
7
193.5
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Intercept
-5.7091
7.9069
-0.7220
0.4974
-25.0567
Buyer Rating
8.5188
2.7759
3.0688
0.0212
1.7265
| Expert Rating | # of cases Purchased |
Solution
1. What is the correlation between rating and purchases? What % of the variation is explained by out linear model?
correlation=sqrt(0.6108) =0.7815369
61.08% of the variation is explained by out linear model
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2 .What are your conclusions about the two types of hypotheses?
Assume that the significant level a=0.05
Since the p-value of F test is 0.022 which is less than 0.05, we reject the null hypothesis that is the regression model is not significant.
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3. Based on the regression, predict the number of cases you could expect to be purchased is a wine has a rating of 2.5.
-5.7091+8.5188*2.5 =15.5879
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4. If asked to predict the number of cases you could expect to be purchased on a wine with a rating of 1.8, what would your response be?
-5.7091+8.5188*1.8 =9.62474
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5. Predict the cases purchased when a wine has a rating of 3.6, how does this compare to the actual purchases for a wine with this rating?
-5.7091+8.5188*3.6 =24.95858
I is closed to the actual purchases for a wine with this rating
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6. Based on residual plot do you go ahead with this linear model or should you consult some statistician who is more knowledgeable about assumptions?
We should consult some statistician who is more knowledgeable about assumptions
