Question

*How well can we evaluate a regression equation “fits” the
data by examining the R Square statistic, and test for statistical
significance of the whole regression equation using the
F-Test?*

Answer #1

1. Compute the regression equation (regression coefficient and
constant) using the same data from the previous question. Compute
the explained variance (R Square) and the standardized regression
coefficient (beta) for this model. For R Square, Sums of Squares
Explained = 235.944; Sums of Squares Total = 520.
2. Given: sample R Square 0.232; SS explained = 2848.62; SS
residual = 9425.25; N = 62. Test the hypotheses Ho: R square = 0;
Ha: R square NE 0 at the .05...

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...

If the R-square of the simple regression of Y on X is 0.5, and
the sample size is 10, and you are testing the hypothesis that X
does not have statistically significant effect on Y at the 5% level
of significance, then the F table value you must be using for this
test is …. .
5.32
4.97
161.5
1.96
5.12

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...

The estimated
regression equation for a model involving two independent variables
and 55 observations is:
y-hat = 55.17 +
1.1X1 - 0.153X2
Other statistics produced for analysis
include:
SSR = 12370.8
SST = 35963.0
Sb1 = 0.33
Sb2 = 0.20
Interpret b1 and b2 in this estimated regression equation
b. Predict y when X1 = 55 and X2 =
70.
Compute R-square and Adjusted R-Square.
e. Compute MSR and MSE.
f. Compute F and use it to test
whether the...

Regression Statistics
Multiple
R
0.3641
R
Square
0.1325
Adjusted
R Square
0.1176
Standard
Error
0.0834
Observations
60
ANOVA
df
SS
MS
F
Significance F
Regression
1
0.0617
0.0617
8.8622
0.0042
Residual
58
0.4038
0.0070
Total
59
0.4655
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-0.0144
0.0110
-1.3062
0.1966
-0.0364
0.0077
X
Variable 1
0.8554
0.2874
2.9769
0.0042
0.2802
1.4307
How do you interpret the above table?

Discuss the strength and the significance of your regression
model by using R-square and significance F where α = 0.05.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.919011822
R
Square
0.844582728
Adjusted R Square
0.834446819
Standard Error
163.953479
Observations
50
ANOVA
df
SS
MS
F
Significance F
Regression
3
6719578.309
2239859.44
83.3257999
1.28754E-18
Residual
46
1236514.191
26880.7433
Total
49
7956092.5
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
21.7335244
114.2095971
0.19029508
0.84991523
-208.158471
251.62552...

Use Data Analysis in Excel to conduct the Regression Analysis to
reproduce the excel out put below (Note: First enter the data in
the next page in an Excel spreadsheet)
Home Sale Price: The table below provides the Excel output of a
regression analysis of the relationship between Home sale price(Y)
measured in thousand dollars and Square feet area
(x):
SUMMARY OUTPUT
Dependent:
Home Price
($1000)
SUMMARY OUTPUT
Dependent:
Home Price
($1000)
Regression Statistics
Multiple R
0.691
R Square
0.478...

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.881644384
R Square
0.77729682
Adjusted R Square
0.767919844
Standard Error
2.046234994
Observations
100
ANOVA
df
SS
MS
F
Significance F
Regression
4
1388.337623
347.0844058
82.89418891
3.94359E-30
Residual
95
397.7723769
4.187077651
Total
99
1786.11
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
30.46621607
3.539611332
8.607220742
1.55786E-13
23.43919912
37.49323302
23.43919912
37.49323302
Engine size
-0.026439837
0.008914999
-2.965769936
0.003818268
-0.044138349
-0.008741326
-0.044138349
-0.008741326
Compression Ratio
0.364901894
0.056081385
6.506649162
3.58903E-09
0.253566269
0.476237519...

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...

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