Consider the following Minitab partial output for the independent variable price
ID: 3361916 • Letter: C
Question
Consider the following Minitab partial output for the independent variable price(in dollars) and the monthly demand for a product( in thousands)
Regression Analysis: Demand(in thousands) versus Price(Dollars)
The regression equation is
Demand(in thousands) = 7.82 - 3.05 Price(Dollars)
Predictor Coef SE Coef
Constant 7.81838 0.04951
Price(Dollars) -3.05487 0.05319
Analysis of Variance
Source DF SS MS
Regression 5.2727
Residual Error
Total 9 5.2855
Predicted Values for New Observations
New
Obs Fit SE Fit 95% CI 95% PI
1 5.2217 0.0129 (5.1919, 5.2515) (5.1248, 5.3186)
Values of Predictors for New Observations
New
Obs Price(Dollars)
1 0.850
Please answer the following questions based on the above Minitab output
1) What is the slope(b1) and what is its interpretation in layman's words? ( 10 points)
2) Perform the test of hypothesis ( t-test) on the following, and state your statistical decision. Use = 0.01 ( 10 points)
H0 : 1 = 0
H1 : 1 0
3) Perform the test of hypothesis (F-test) on the following, and state your statistical decision. Use = 0.01 ( 10 points)
H0 : 1 = 0
H1 : 1 0
4) What is the coefficient of determination (r2) i.e., percentage of variability in demand explained by the independent variable price? ( 10 points)
5) What is the 95% Prediction Interval estimate for the monthly demand when the price X is set to $0.85 ( i.e.,YX=$0.85) ? ( 10 points)
Explanation / Answer
1) What is the slope(b1) and what is its interpretation in layman's words?
slope(b1) = -3.05487
As price increases by $1, demand decreases by $3054.87.
2) Perform the test of hypothesis ( t-test) on the following, and state your statistical decision. Use = 0.01.
H0 : 1 = 0
H1 : 1 0
test statistic= slope/SE=-3.05487/0.05319 = -57.43
Test statistic is too large, we reject the null hypothesis. There is sufficient evidence that slope is significant.
3) Perform the test of hypothesis (F-test) on the following, and state your statistical decision. Use = 0.01
H0 : 1 = 0
H1 : 1 0
The complete ANOVA table is shown below:
p-value is extremely small, we reject the null hypothesis. There is sufficient evidence that slope is significant.
4) What is the coefficient of determination (r2) i.e., percentage of variability in demand explained by the independent variable price?
r2=SSR/SST=5.2727/5.2855=0.9976=99.76%
99.76% of variability in demand explained by the independent variable price.
5) What is the 95% Prediction Interval estimate for the monthly demand when the price X is set to $0.85 ( i.e.,YX=$0.85) ?
(5.1248, 5.3186)
ANOVA df SS MS F Significance F Regression 1 5.2727 5.2727 3295.438 0.000 Residual 8 0.0128 0.0016 Total 9 5.2855Related Questions
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