Question

The Regression Coefficient (b) = | |||

**The Y-Intercept (a) = |
|||

The Adjusted Coefficient of Determination (R^2)
= |
|||

The Coeffefficient of Correlation (r ) = | |||

F-Ratio = | |||

Predict the Attendance Rate when | |||

there is a Welfare Rate of 15 Cases = | |||

Regression Statistics |
NOTE: Yellow Cells (NA = Not Available) have been intentionally provided without values. | ||||||

Multiple R | 0.788542385 | All of the information that you need to complete the questions is on this page. | |||||

R Square | NA | All answers are to be on the YOUR ANSWERS HERE worksheet.. | |||||

Adjusted R Square | NA | ||||||

Standard Error | 0.622829992 | ||||||

Observations | 92 | Your | |||||

ANOVA | |||||||

df |
SS |
MS |
F |
Significance F |
|||

Regression | 1 | 57.39962601 | NA | NA | 1.05069E-20 | ||

Residual | 90 | 34.91254791 | NA | ||||

Total | 91 | 92.31217391 | |||||

Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
||

Intercept | NA | 0.098517084 | 975.6544 | 6.6998E-183 | 95.92290199 | 96.31434444 | |

Welfare | -0.1220211 | 0.010031131 | -12.16424 | 1.05069E-20 | -0.141949674 | -0.10209252 |

Answer #1

The Regression Coefficient (b)
= **-0.1220211**

The Y-Intercept (a) = t_{stat} * Standard error
= 975.6544 * 0.098517084 =
**96.11862648**

Coefficient of Determination, R^{2} =
(0.788542385)^{2} = **0.621799093**

The Adjusted Coefficient of Determination (R^2) = 1-
(1-R^{2})*(N-1) / (N-k-1)

= (1-0.621799093)*(91) / (90) = **0.617596861**

The Coeffefficient of Correlation (r )
= **0.788542385**

F-Ratio = (SS_{regression} / df_{regression} ) /
(SS_{residual} / df_{residual} )

= ( 57.39962601 / 1) / ( 34.91254791 / 90) =
**147.9687577**

Predict the Attendance Rate when there is a Welfare Rate of 15
Cases = 96.11862648 - 0.1220211*15 =
**94.28830998**

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?

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...

Regression Statistics
Multiple
R
0.710723
R
Square
0.505127
Adjusted
R Square
0.450141
Standard
Error
1.216847
Observations
21
ANOVA
df
SS
MS
F
Significance F
Regression
2
27.20518
13.60259
9.186487
0.00178
Residual
18
26.65291
1.480717
Total
20
53.8581
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
58.74307
12.66908
4.636728
0.000205
32.12632
85.35982
32.12632
85.35982
High
School Grad
-0.00133
0.000311
-4.28236
0.000448
-0.00198
-0.00068
-0.00198
-0.00068
Bachelor's
-0.00016
5.46E-05
-3.00144
0.007661
-0.00028
-4.9E-05
-0.00028
-4.9E-05...

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...

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...

According to the Data, is the regression a better fit than the
one with the Dummy variable, explain?
Regression Statistics
Multiple R
0.550554268
R Square
0.303110002
Adjusted R Square
0.288887757
Standard Error
2.409611727
Observations
51
ANOVA
df
SS
MS
F
Significance F
Regression
1
123.7445988
123.7445988
21.31238807
2.8414E-05
Residual
49
284.5052051
5.806228676
Total
50
408.2498039
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Intercept
5.649982553
1.521266701
3.713998702
0.000522686
2.592882662
U-rate
1.826625993
0.395670412
4.616534206
2.84144E-05
1.0314965
Multiple R
0.572568188
R Square...

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...

] A partial computer output from a regression analysis using
Excel’s Regression tool follows. Regression Statistics Multiple R
(1) R Square 0.923 Adjusted R Square (2) Standard Error 3.35
Observations ANOVA df SS MS F Significance F Regression (3) 1612
(7) (9) Residual 12 (5) (8) Total (4) (6) Coefficients Standard
Error t Stat P-value Intercept 8.103 2.667 x1 7.602 2.105 (10) x2
3.111 0.613 (11)

Calculate the following statistics given the existing
information (1 point per calculation):
Regression Statistics
Multiple R
R Square
Adjusted R Square
0.559058
Standard Error
Observations
30
ANOVA
df
SS
MS
F
Significance F
Regression
2
3609132796
19.38411515
6.02827E-06
Residual
27
2513568062
Total
29
6122700857
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-15800.8
57294.51554
-0.27578
0.784814722
CARAT
12266.83
1999.250369
6.135715
1.48071E-06
DEPTH
156.686
928.9461882
0.168671
0.867312915
Additionally interpret your results. Be sure to comment on
Accuracy, significance...

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.993709623
R Square
0.987458816
Adjusted R Square
0.987378251
Standard Error
514.2440271
Observations
471
ANOVA
df
SS
MS
F
Significance F
Regression
3
9723795745
3241265248
12256.7707
0
Residual
467
123496711.4
264446.9194
Total
470
9847292456
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-267.1127974
42.01832073
-6.357055513
4.8988E-10
-349.68118
-184.54441
-349.68118
-184.54441
Fuel cost (000,000)
0.449917223
0.098292092
4.577349137
6.0451E-06
0.25676768
0.64306676
0.25676768
0.64306676
Salary (000,000)
-0.327915884
0.188252958
-1.741889678
0.08218614
-0.6978436...

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