Question

f. Interpret the slope coefficient for one of the dummy variables included in your regression model.

g. For the slope coefficient of the variable with the smallest slope coefficient (ignore sign, use absolute value), test to see if the “a priori” expectation from part (a) is confirmed. Use alpha = 0.05.

h. Interpret the coefficient of determination in this situation.

i. Test the explanatory power of the entire regression model. Please use alpha = 0.01.

j. For the variable with the largest estimated slope coefficient (ignore sign, use absolute value), construct a 90% confidence interval for the corresponding population slope coefficient.

k. Interpret the interval constructed in part (j).

l. What is the p-value associated with the model test in this situation?

m. Create the normal probability plot associated with your multiple regression model. Is the information displayed in the plot consistent with the associated error term assumption made in the model?

here is the regression summary

Regression Statistics | ||||||||

Multiple R | 0.554741323 | |||||||

R Square | 0.307737935 | |||||||

Adjusted R Square | 0.296037732 | |||||||

Standard Error | 30.54182977 | |||||||

Observations | 362 | |||||||

ANOVA | ||||||||

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

Regression | 6 | 147207.169 | 24534.5281 | 26.3019293 | 6.9183E-26 | |||

Residual | 355 | 331145.195 | 932.803366 | |||||

Total | 361 | 478352.364 | ||||||

Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |

Intercept | 113.393156 | 11.4315172 | 9.91934437 | 1.245E-20 | 90.9111467 | 135.875165 | 90.9111467 | 135.875165 |

LOTSIZE | -1.211020711 | 0.32740277 | -3.6988713 | 0.00025085 | -1.8549136 | -0.5671279 | -1.8549136 | -0.5671279 |

AGE | -0.24182222 | 0.14233746 | -1.6989359 | 0.09020736 | -0.5217529 | 0.03810843 | -0.5217529 | 0.03810843 |

RMS | 10.76999883 | 1.24970453 | 8.6180362 | 2.2783E-16 | 8.31224382 | 13.2277538 | 8.31224382 | 13.2277538 |

MOD KITCH | 3.938467175 | 6.02621357 | 0.65355586 | 0.51382108 | -7.9130996 | 15.790034 | -7.9130996 | 15.790034 |

MOD BATH | 7.070026791 | 6.04449449 | 1.16966387 | 0.24292097 | -4.8174925 | 18.9575461 | -4.8174925 | 18.9575461 |

AIRCON | 33.00755236 | 6.06897927 | 5.43873209 | 1.0009E-07 | 21.0718796 | 44.9432251 | 21.0718796 | 44.9432251 |

Answer #1

h)

coefficient of determination = r^2

= 0.307737

it means that 30.77 % of variation in dependent variable is explained by independent variable

i)

significance F =6.9183E-26 << 0.01

hence the model is significant

j)

largest slope coefficient = 33.00755236 for AIRCON

se = 6.068979

t = 1.645 for 90 % CI

hence

90 % confidence interval

( 33.00755236 - 1.645 * 6.068979, 33.00755236 + 1.645 *
6.068979)

= (23.024081905,42.99102)

k)

we are 90 % confident that true slope lies in this CI

l)

p-value = 6.9183E-26

Using this regression model below that I created to, interpret
the slope estimates, that is interpret the impact that income [per
capita gross national income] has on U5MR [No. of deaths of
children 0-5 years old, per 1000 live births]. Then interpret the r
square [for example what % of the variation can be explained by the
other variable]. Lastly calculate the predicted values of U5MR when
income = $10,000.
Regression Statistics
Multiple
R
0.443388
R
Square
0.196593
Adj R...

Discuss the model and interpret the results: report overall
model fit (t and significance), report the slope coefficient and
significance, report and interpret r squared.
Regression
Statistics
Multiple R
0.001989374
R Square
3.95761E-06
Adjusted R
Square
-0.005046527
Standard Error
8605.170404
Observations
200
ANOVA
df
SS
MS
F
Significance
F
Regression
1
58025.4985
58025.4985
0.00078361
0.977695901
Residual
198
14661693620
74048957.68
Total
199
14661751645
Coefficients
Standard Error
t
Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
15668.85874
2390.079111
6.555790838...

Use the regression model I created below for U5MR [No. of deaths
of children 0-5 yrs old per 1000 live births] and Female Youth LR
[Percent of females 15-24 literate] to answer this question.
Interpret the slope estimates that is interpret the impact Female
Youth LR has on U5MR, then interpret the r square for example what
% of what variation can be explained by what variable. Lastly
calculate the predicted values U5MR when Female Youth LR= 80.
Regression Statistics...

Identify and interpret the F test (one paragraph):
Using the p-value approach, is the null hypothesis for the F
test rejected or not rejected? Why or why not?
Interpret the implications of these findings for the
model.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.60
R Square
0.36
Adjusted R Square
0.26
Standard Error
9.25
Observations
30.00
ANOVA
df
SS
MS
F
Significance F
Regression
4.00
1212.46
303.12
3.54
0.02
Residual
25.00
2139.14
85.57
Total
29.00
3351.60
Coefficients
Standard Error
t...

Use Excel to develop a regression model for the Hospital
Database (using the “Excel Databases.xls” file on Blackboard) to
predict the number of Personnel by the number of Births. Perform a
test of the slope. What is the value of the test statistic? Write
your answer as a number, round your answer to 2 decimal places.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.697463374
R
Square
0.486455158
Adjusted R Square
0.483861497
Standard Error
590.2581194
Observations
200
ANOVA
df
SS
MS
F...

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...

interpret each coefficient estimate and discuss its significance
using α = 0.01, α = 0.05 and α = 0.10. Use the concepts of strict
and weak significance too
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.820140129
R
Square
0.672629832
Adjusted R Square
0.658699186
Standard Error
235.4076294
Observations
50
ANOVA
df
SS
MS
F
Significance F
Regression
2
5351505.158
2675752.58
48.2841827
4.0125E-12
Residual
47
2604587.342
55416.752
Total
49
7956092.5
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper...

Use this regression model I created to answer to answer this
question it has 2 parts:
2. (a) Interpret the slope estimates in this regression model,
that is interpret the impact Female Youth LR on U5MR, and interpret
the R2 [square] respectively.
(b) Using the results for this regression model, the predicted
value of U5MR(U5MR-No. of deaths of children 0-5 yrs, per 1000 live
births) when Female Youth LR =80. (Female Youth LR-Percent of
females 15-24 literate)
Regression Statistics
Multiple...

7) Identify and interpret the adjusted R2 (one paragraph):
What does the value of the adjusted R2 reveal about the
model?
If the adjusted R2 is low, how has the choice of independent
variables created this result?
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.60
R Square
0.36
Adjusted R Square
0.26
Standard Error
9.25
Observations
30.00
ANOVA
df
SS
MS
F
Significance F
Regression
4.00
1212.46
303.12
3.54
0.02
Residual
25.00
2139.14
85.57
Total
29.00
3351.60
Coefficients
Standard Error
t...

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...

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