Consider the following output from a regression analysis: Multiple R 0.98223752
ID: 2921927 • Letter: C
Question
Consider the following output from a regression analysis:
Multiple R
0.98223752
R Square
0.96479055
Adjusted R Square
0.95518798
Standard Error
0.23310465
Observations
15
df
SS
MS
F
Significance F
Regression
3
16.37828444
5.459428
100.4721
2.82244E-08
Residual
11
0.597715562
0.054338
Total
14
16.976
Coefficients
Standard Error
t Stat
P-value
Intercept
3.98076893
1.573044228
2.530615
0.027943
X1
0.07321648
0.020889718
3.504905
0.004928
X2
-0.0323216
0.020895785
-1.5468
0.150182
X3
-0.0038861
0.003833348
-1.01376
0.332478
The output shows that:
A.) the overall model is significant at an alpha level of 0.05.
B.) 95% of the residuals are within + 0.2331.
C.) The coefficient of multiple determination for this model is 0.9822.
D.) All of the above statements are true.
If the relationship between y (a dependent variable) and x (an independent variable) is curvilinear as suggested by a graph, the regression equation representing the curvilinear relationship will contain:
some complex terms
no higher order terms
only a first order term
a first-order and a second-order term
Multiple R
0.98223752
R Square
0.96479055
Adjusted R Square
0.95518798
Standard Error
0.23310465
Observations
15
df
SS
MS
F
Significance F
Regression
3
16.37828444
5.459428
100.4721
2.82244E-08
Residual
11
0.597715562
0.054338
Total
14
16.976
Coefficients
Standard Error
t Stat
P-value
Intercept
3.98076893
1.573044228
2.530615
0.027943
X1
0.07321648
0.020889718
3.504905
0.004928
X2
-0.0323216
0.020895785
-1.5468
0.150182
X3
-0.0038861
0.003833348
-1.01376
0.332478
Explanation / Answer
1) A.) the overall model is significant at an alpha level of 0.05.
The signficance F is less than 0.05
Standard error is 0.2331, it does not mean 95% of residuals are within 0.2331.
In multiple regression, the multiple R is the coefficient of multiple correlation, whereas its square is the coefficient of determination
2)
a first-order and a second-order term
D.)a first-order and a second-order term