Question

Hi,

In the multiple regression output I got R-squared 0.52387 or
52.4% and adjusted R-squared 0.2858 (28.6%).

Is the regression model good or bad, can it be used to
forecast the dependent variable?

Answer #1

Solution:

The given values of R-squared derived for the multiple regression are too low. A relatively strong or good R-squared value is considered to be at least 70% or 0.70, for academic regressions (for research purpose, any value above 50% is also considered to be good enough). So, the regression model is not good.

With such low value for adjusted R-squared, there is a possibility that your regression model includes some of the explanatory variables which are an extra burden, meaning they do not explain the dependent variable well and thus, must be eliminated (which would not decrease R-squared value by much, but increase adjusted R-squared). No, it's not good enough, or better, strong enough model to build forecasts about the dependent variable.

I did a multiple regression analysis of some data and got a
multiple R squared value of 0.07004 and an overall p value of
0.7479. What does this mean?

What is the relationship between R-squared and the adjusted
R-squared?
a.the adjusted R-squared is larger than regular R-squared
b. for a simple linear regression the adjusted R-squared is
equal to regular R-squared
c. the adjusted R-squared adjusts explanatory power by the
degrees of freedom
d. the adjusted R-squared adjusts explanatory power by division
by the standard error of each coefficient
e. the adjusted R-squared always increases as more independent
variables are added to the model

A regression analysis was performed and the summary output is
shown below.
Regression Statistics
Multiple R
0.7149844700.714984470
R Square
0.5112027920.511202792
Adjusted R Square
0.4904029110.490402911
Standard Error
8.2079903998.207990399
Observations
5050
ANOVA
dfdf
SSSS
MSMS
FF
Significance FF
Regression
22
3311.5863311.586
1655.7931655.793
24.577224.5772
4.9491E-084.9491E-08
Residual
4747
3166.4423166.442
67.37167.371
Total
4949
6478.0286478.028
Step 1 of 2:
How many independent variables are included in the regression
model?
Step 2 of 2:
Which measure is appropriate for determining the proportion of
variation in the dependent...

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.870402
R
Square
0.7576
Adjusted R Square
0.68488
Standard Error
1816.52
Observations
27
ANOVA
df
SS
MS
F
Significance F
Regression
6
2.06E+08
34376848
10.41804
2.81E-05
Residual
20
65994862
3299743
Total
26
2.72E+08
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-4695.4
12622.97
-0.37197
0.713825
-31026.5
21635.66
-31026.5
21635.66
AGE
161.7028
126.5655
1.277621
0.216015
-102.308
425.7137
-102.308
425.7137
MILAGE
-0.03441
0.023186
-1.4842
0.153346
-0.08278
0.013953
-0.08278
0.013953...

Is this statement true or false? Adjusted R-squared is more
accurate for models with multiple independent variables because
R-squared tends to underestimate the effect of additional
variables.

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.909785963
R
Square
0.827710499
Adjusted R Square
0.826591736
Standard Error
7.177298036
Observations
156
ANOVA
df
SS
MS
F
Significance F
Regression
1
38112.05194
38112.05194
739.8443652
1.09619E-60
Residual
154
7933.095493
51.5136071
Total
155
46045.14744
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
8.67422449
2.447697434
3.543830365
0.000522385
3.838827439
13.50962154
3.838827439
13.50962154
X
Variable 1
0.801382837
0.029462517
27.20008024
1.09619E-60
0.743179986
0.859585688
0.743179986
0.859585688
(d)
How much of the variation in...

Regression
Statistics
Multiple R
0.983211253
R Square
0.966704367
Adjusted R Square
0.962542413
Standard Error
234.8326064
Observations
10
what can you conclude with this regression?

SUMMARY OUTPUT Regression Statistics Multiple R 0.84508179 R
Square 0.714163232 Adjusted R Square 0.704942691 Standard Error
9.187149383 Observations 33 ANOVA df SS MS F Significance F
Regression 1 6537.363661 6537.363661 77.4535073 6.17395E-10
Residual 31 2616.515127 84.40371378 Total 32 9153.878788
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Lower 95.0% Upper 95.0% Intercept 61.07492285 3.406335763
17.92980114 6.41286E-18 54.12765526 68.02219044 54.12765526
68.02219044 Time (Y) -0.038369095 0.004359744 -8.800767426
6.17395E-10 -0.047260852 -0.029477338 -0.047260852 -0.029477338
Using your highlighted cells, what is the equation...

SUMMARY OUTPUT Regression Statistics Multiple R 0.440902923 R
Square 0.194395388 Adjusted R Square 0.165100675 Standard Error
0.428710255 Observations 115 ANOVA df SS MS F Significance F
Regression 4 4.878479035 1.219619759 6.635852231 8.02761E-05
Residual 110 20.21717314 0.183792483 Total 114 25.09565217
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Lower 95.0% Upper 95.0% Intercept 0.321875686 0.323939655
0.99362854 0.322584465 -0.320096675 0.963848047 -0.320096675
0.963848047 Gender -0.307211858 0.082630734 -3.717888514
0.000317832 -0.470966578 -0.143457137 -0.470966578 -0.143457137 Age
0.000724105 0.091134233 0.007945479 0.993674883 -0.179882553
0.181330763 -0.179882553 0.181330763...

SUMMARY OUTPUT
Dependent
X variable:
all other variables
Regression Statistics
Independent
Y variable:
oil usage
Multiple R
0.885464
R
Square
0.784046
variation
Adjusted R Square
0.76605
Standard Error
85.4675
Observations
40
ANOVA
df
SS
MS
F
Significance F
Regression
3
954738.9
318246.3089
43.56737
4.55E-12
Residual
36
262969
7304.693706
Total
39
1217708
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-218.31
63.95851
-3.413304572
0.001602
-348.024
-88.596
-348.024
-88.596
Degree Days
0.275079
0.036333
7.571119093
5.94E-09...

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