7. A computer manufacturer has developed a regression model relating his sales (
ID: 3222081 • Letter: 7
Question
7. A computer manufacturer has developed a regression model relating his sales (y in $10,000s) with three independent variables. The three independent variables are price per unit (Price in $100s), advertising (ADV in $1000s), and the number of product lines (Lines). Part of the regression results is shown below.
Coefficients
Standard Error
Intercept
1.0211
22.8752
Price
-0.1524
0.1411
ADV
0.8849
0.2886
Lines
-0.1463
1.5340
ANOVA
Source
df
SS
Regression
2708.61
Error (Residuals)
14
2840.51
a.
Use the above results and write the regression equation that can be used to predict sales.
b.
If the manufacturer has 10 product lines, incurring an advertising cost of $40,000, with the price per unit being $3000, what is your estimate of their sales? Give your answer in dollars.
c.
Compute the multiple coefficient of determination and fully interpret its meaning.
d.
At = .05, test to see if there is a significant relationship between sales and unit price.
e.
Is the regression model significant at = .05? (Perform an F test.)
f.
Fully interpret the meaning of the regression coefficient (slope) of price per unit. Discuss.
7. A computer manufacturer has developed a regression model relating his sales (y in $10,000s) with three independent variables. The three independent variables are price per unit (Price in $100s), advertising (ADV in $1000s), and the number of product lines (Lines). Part of the regression results is shown below.
Coefficients
Standard Error
Intercept
1.0211
22.8752
Price
-0.1524
0.1411
ADV
0.8849
0.2886
Lines
-0.1463
1.5340
ANOVA
Source
df
SS
Regression
2708.61
Error (Residuals)
14
2840.51
a.
Use the above results and write the regression equation that can be used to predict sales.
b.
If the manufacturer has 10 product lines, incurring an advertising cost of $40,000, with the price per unit being $3000, what is your estimate of their sales? Give your answer in dollars.
c.
Compute the multiple coefficient of determination and fully interpret its meaning.
d.
At = .05, test to see if there is a significant relationship between sales and unit price.
e.
Is the regression model significant at = .05? (Perform an F test.)
f.
Fully interpret the meaning of the regression coefficient (slope) of price per unit. Discuss.
Explanation / Answer
a.
Use the above results and write the regression equation that can be used to predict sales.
The regression equation can be formed using the coefficients column as
sales = 1.0211 + 0.8849*ADV - 0.1524*Price - 0.1463*Lines
b.
If the manufacturer has 10 product lines, incurring an advertising cost of $40,000, with the price per unit being $3000, what is your estimate of their sales? Give your answer in dollars.
sales = 1.0211 + 0.8849*ADV - 0.1524*Price - 0.1463*Lines , using the regresion equation and putting the values we get
sales = 1.0211 + 0.8849*40000 - 0.1524*3000 - 0.1463*10 = 34938.35
c.
Compute the multiple coefficient of determination and fully interpret its meaning.
r2 = SSR/SStotal = 2708.61/(2708.61+2840.51) = 0.4881 , hence the model is able to capture only 48.81% variation in the data
d.
At = .05, test to see if there is a significant relationship between sales and unit price.
we calculate t value as coefficient/SE , and then the t values are compared against the p values .
The P-Value is .475527 for given t value and df = 17-1 = 16
The P-Value is .296154.
The result is not significant at p < .05.
e.
Is the regression model significant at = .05? (Perform an F test.)
df(Regression) = # of predictor variables , so there are 3 predictors
0.02148828
now the MS values are calculated by deviding SS with respective df .
we check the p value from the F table and this comes out to be 0.021 , which is less than 0.05 , hence the model is significant
f.
Fully interpret the meaning of the regression coefficient (slope) of price per unit. Discuss.
sales = 1.0211 + 0.8849*ADV - 0.1524*Price - 0.1463*Lines
this means that for every unit change in the price value the sales would go down by 0.1524 units.
Hope this helps !! Please rate !!
a.
Use the above results and write the regression equation that can be used to predict sales.
The regression equation can be formed using the coefficients column as
sales = 1.0211 + 0.8849*ADV - 0.1524*Price - 0.1463*Lines
b.
If the manufacturer has 10 product lines, incurring an advertising cost of $40,000, with the price per unit being $3000, what is your estimate of their sales? Give your answer in dollars.
sales = 1.0211 + 0.8849*ADV - 0.1524*Price - 0.1463*Lines , using the regresion equation and putting the values we get
sales = 1.0211 + 0.8849*40000 - 0.1524*3000 - 0.1463*10 = 34938.35
c.
Compute the multiple coefficient of determination and fully interpret its meaning.
r2 = SSR/SStotal = 2708.61/(2708.61+2840.51) = 0.4881 , hence the model is able to capture only 48.81% variation in the data
d.
At = .05, test to see if there is a significant relationship between sales and unit price.
Coefficients Standard Error t value Intercept 1.0211 22.8752 0.044638 Price -0.1524 0.1411 -1.08009 ADV 0.8849 0.2886 3.066182 Lines -0.1463 1.534 -0.09537we calculate t value as coefficient/SE , and then the t values are compared against the p values .
The P-Value is .475527 for given t value and df = 17-1 = 16
The P-Value is .296154.
The result is not significant at p < .05.
e.
Is the regression model significant at = .05? (Perform an F test.)
df(Regression) = # of predictor variables , so there are 3 predictors
Source df SS MS F VALUE significant F Regression 3 2708.61 902.87 4.4499680.02148828
Error (Residuals) 14 2840.51 202.8936now the MS values are calculated by deviding SS with respective df .
we check the p value from the F table and this comes out to be 0.021 , which is less than 0.05 , hence the model is significant
f.
Fully interpret the meaning of the regression coefficient (slope) of price per unit. Discuss.
sales = 1.0211 + 0.8849*ADV - 0.1524*Price - 0.1463*Lines
this means that for every unit change in the price value the sales would go down by 0.1524 units.
Hope this helps !! Please rate !!
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