Question

A regression analysis was performed and the summary output is shown below.

Multiple R | 0.7149844700.714984470 |
---|---|

R Square | 0.5112027920.511202792 |

Adjusted R Square | 0.4904029110.490402911 |

Standard Error | 8.2079903998.207990399 |

Observations | 5050 |

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 variable explained by the set of independent variable(s) in this model?

Answer #1

(1) Degree of freedom for regression = 2

and we know that number of independent variable =df(regression) + 1

independent variables = 2 + 1 = 3

So, we have 3 independent variables in regression model.

(2) R square is appropriate for determining the proportion of variation in the dependent variable explained by the set of independent variable(s) in this model

Given that R square = 0.5112

this means that 51.12% of variation in the dependent variable explained by the set of independent variable(s) in this model

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...

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...

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...

Using the attached regression output, answer the
following:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.972971
R Square
0.946673
Adjusted R Square
0.944355
Standard Error
76.07265
Observations
49
ANOVA
df
SS
MS
F
Significance F
Regression
2
4725757
2362878
408.3046
5.24E-30
Residual
46
266204.2
5787.049
Total
48
4991961
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-0.46627
14.97924
-0.03113
0.975302
-30.6179
29.68537
X1
0.09548
0.084947
1.123997
0.266846
-0.07551
0.26647
X2
0.896042
0.205319
4.364141
7.16E-05
0.482756
1.309328
a. What...

The following regression output is available. Notice that some
of the values are missing.
Regression Statistics
Multiple R
0.754525991
Adjusted R Square
0.507782253
Standard Error
ANOVA
df
SS
MS
Regression
1
Residual
7
27.3727758
3.910397
Total
8
63.55555556
Coefficients
Standard Error
Intercept
4.822953737
2.20457789
X
0.053825623
0.017694916
Pt 1. Given this information, what is the standard error of the
estimate for the regression model?
Pt 2. Given this information, what was the sample
size used in the study?
Pt 3....

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
Regression Statistics
Multiple
R
0.231960777
R
Square
0.053805802
Adjusted
R Square
0.034093423
Standard
Error
5272.980333
Observations
50
ANOVA
df
SS
MS
F
Significance F
Regression
1
75893113.09
75893113.09
2.729543781
0.105035125
Residual
48
1334607437
27804321.59
Total
49
1410500550
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 99.0%
Upper 99.0%
Intercept
6396.894057
3281.342486
1.949474669
0.057094351
-200.6871963
12994.47531
-2404.335972
15198.12409
HSRANK
64.68225855
39.15075519
1.6521331
0.105035125
-14.03561063
143.4001277
-40.32805468
169.6925718
a. According to your estimate, what is the predicted...

Dep.=
Mileage
Indep.=
Length
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
7.0000
ANOVA
Significance
df
SS
MS
F
F
Regression
6.1135
Residual
Total
169.4286
Standard
Coefficients
Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
80.0094
Length
-0.3047
SE
CI
CI
PI
PI
Predicted
Predicted
Lower
Upper
Lower
Upper
x0
Value
Value
95%
95%
95%
95%
175.0000
2.3108
210.0000
2.9335
Is there a relationship between a car's gas
MILEAGE (in miles/gallon) and its...

Dep.=
Mileage
Indep.=
Cylinders
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
7.0000
ANOVA
Significance
df
SS
MS
F
F
Regression
12.4926
Residual
Total
169.4286
Standard
Coefficients
Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
38.7857
Cylinders
-2.7500
SE
CI
CI
PI
PI
Predicted
Predicted
Lower
Upper
Lower
Upper
x0
Value
Value
95%
95%
95%
95%
4.0000
1.9507
6.0000
1.1763
Is there a relationship between a car's gas
MILEAGE (in miles/gallon) and its...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 11 minutes ago

asked 29 minutes ago

asked 30 minutes ago

asked 30 minutes ago

asked 32 minutes ago

asked 39 minutes ago

asked 54 minutes ago

asked 56 minutes ago

asked 56 minutes ago

asked 56 minutes ago

asked 56 minutes ago