See below The Excel output for this exercise is given below. Use this output to
ID: 3297678 • Letter: S
Question
See below The Excel output for this exercise is given below. Use this output to answer the questions.
a) State the Multiple Regression Equation.
b) Interpret the meaning of the slopes of this equation
c)Predict the gasoline mileage for an automobile that has a length of 195 inches and a weight of 3000 pounds.
e)Is there a significant relationship between the gasoline mileage and the two independent variables (Length and weight) at the 0.05 level of significance?
g) Interpret the meaning of the coefficient of multiple determination in this problem
i) At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.
k) Construct a 95% confidence interval estimate of the population slope between gasoline mileage and weight.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.782187748
R Square
0.611817673
Adjusted R Square
0.60186428
Standard Error
2.952425134
Observations
121
ANOVA
df
SS
MS
F
Significance F
Regression
3
1607.421998
535.8073326
61.46825227
6.20871E-24
Residual
117
1019.867258
8.716814173
Total
120
2627.289256
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
42.43290086
8.218578926
5.163045977
1.00728E-06
26.15643651
58.70936521
Length
-0.00667189
0.036217633
-0.18421688
0.854162226
-0.07839902
0.065055222
Width
-0.03989444
0.182924039
-0.21809293
0.827736634
-0.40216590
0.322377022
Weight
-0.00487697
0.000600754
-8.11807648
5.3858E-13
-0.00606673
-0.00368720
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.782187748
R Square
0.611817673
Adjusted R Square
0.60186428
Standard Error
2.952425134
Observations
121
ANOVA
df
SS
MS
F
Significance F
Regression
3
1607.421998
535.8073326
61.46825227
6.20871E-24
Residual
117
1019.867258
8.716814173
Total
120
2627.289256
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
42.43290086
8.218578926
5.163045977
1.00728E-06
26.15643651
58.70936521
Length
-0.00667189
0.036217633
-0.18421688
0.854162226
-0.07839902
0.065055222
Width
-0.03989444
0.182924039
-0.21809293
0.827736634
-0.40216590
0.322377022
Weight
-0.00487697
0.000600754
-8.11807648
5.3858E-13
-0.00606673
-0.00368720
Explanation / Answer
a]
From above analysis
Multiple Regression Equation is Gasoline mileage = 42.4329 - 0.00667Length - 0.03989Width - 0.004877Weight
b]
Interpret the meaning of the slopes of this equation
Slope of Length: if gasoline mileage increase by 1 unit then length is decrease by approximately 0.00667 units.
Slope of Width: if gasoline mileage increase by 1 unit then width is decrease by approximately 0.03989 units.
Slope of Weight: if gasoline mileage increase by 1 unit then Weight is decrease by approximately 0.004877 units.
c) Predict the gasoline mileage for an automobile that has a length of 195 inches and a weight of 3000 pounds.
gasoline mileage = 42.4329 - 0.00667*195 - 0.004877*3000 = 26.50
e) Is there a significant relationship between the gasoline mileage and the two independent variables (Length and weight) at the 0.05 level of significance.
Yes becuase p-value of the regression model is very small compared with 0.05 level of significance. Hence indicates that you can reject the null hypothesis. ( the coefficient is equal to zero (no effect) ).
At 0.05 level of significance, there is a significant relationship between the gasoline mileage and the two independent variables (Length and weight).