20 2 60 4 46 3 41 2 12 1 137 10 68 5 89 5 4 1 32 2 144 9 156 10 93 6 36 3 72 4 1
ID: 2926279 • Letter: 2
Question
20 2 60 4 46 3 41 2 12 1 137 10 68 5 89 5 4 1 32 2 144 9 156 10 93 6 36 3 72 4 100 8 105 7 131 8 127 10 57 4 66 5 101 7 109 7 74 5 134 9 112 7 18 2 73 5 111 7 96 6 123 8 90 5 20 2 28 2 3 1 57 4 86 5 132 9 112 7 27 1 131 9 34 2 27 2 61 4 77 5 20 2 60 4 46 3 41 2 12 1 137 10 68 5 89 5 4 1 32 2 144 9 156 10 93 6 36 3 72 4 100 8 105 7 131 8 127 10 57 4 66 5 101 7 109 7 74 5 134 9 112 7 18 2 73 5 111 7 96 6 123 8 90 5 20 2 28 2 3 1 57 4 86 5 132 9 112 7 27 1 131 9 34 2 27 2 61 4 77 5 #3.13. Refer to Copier maintenance Problem 1.20. a. What are the alternative conclusions when testing for lack of fit of a linear regression b. Perform the test indicated in part (a). Control the risk of Type Ierror at.05. State the decision c. Does the test in part (b) detect other departures from regression model (2.1), such as lack function? rule and conclusion. of constant variance or lack of normality in the error terms? Could the results of the test of lack of fit be affected by such departures? Discuss.Explanation / Answer
Once we start building a linear regression model, first of all its performance depends on various constants. If the error term shows departure from normality, the regression model cannot give better performance. Response variable should be normally distributed. For testing that, we commonly make use of shapro wilk test or Kolmogirov Smirnov test test or simply using qqplots to check that. We check that the there should not be auto-correlation. One of the basic assumption which we check is Homoscedasticity ( means equality of variances check using Levenes test).
If we build a linear regression model as for data in Table 1.
Here we have considered, Variable 1 as response variable and Variable 2 as independent variable.
Two alternative methods for testing whether a linear association exists between the predictor x and the response y in a simple linear regression model are
F test and T test tells us how formally how well the model fits the data.
If we take our data set and start building a model using simply excel data analysis tool pack.
Table 1: Data
Variable1
Variable 2
20.00
2.00
60.00
4.00
46.00
3.00
41.00
2.00
12.00
1.00
137.00
10.00
68.00
5.00
89.00
5.00
4.00
1.00
32.00
2.00
144.00
9.00
156.00
10.00
93.00
6.00
36.00
3.00
72.00
4.00
100.00
8.00
105.00
7.00
131.00
8.00
127.00
10.00
57.00
4.00
66.00
5.00
101.00
7.00
109.00
7.00
74.00
5.00
134.00
9.00
112.00
7.00
18.00
2.00
73.00
5.00
111.00
7.00
96.00
6.00
123.00
8.00
90.00
5.00
20.00
2.00
28.00
2.00
3.00
1.00
57.00
4.00
86.00
5.00
132.00
9.00
112.00
7.00
27.00
1.00
131.00
9.00
34.00
2.00
27.00
2.00
61.00
4.00
77.00
5.00
Test of Homogeneity of Variances
Variable 1
Levene Statistic
df1
df2
Sig.
109.423
1
88
.000
After performing homogeneity test on data in table 1.
Levene Statistic P value (<0.05) tells us that there is no homogeneity in the variances in the two variables.
ANOVA
Variable two
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
113920.044
1
113920.044
124.199
.000
Within Groups
80717.244
88
917.241
Total
194637.289
89
Using Excel data analysis tool to see the model coefficients significance.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.978517
R Square
0.957495
Adjusted R Square
0.956507
Standard Error
8.913508
Observations
45
ANOVA
df
SS
MS
F
Significance F
Regression
1
76960.42
76960.42298
968.6572
0.0000
Residual
43
3416.377
79.45062845
Total
44
80376.8
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-0.58016
2.803941
-0.206907577
0.837059
-6.234842727
5.074529412
B
15.03525
0.483087
31.12325812
0.000
14.06100984
16.00948624
R2 tells us how much variation independent variable explains regarding variation in dependent variable. The model intercept is insignificant ( means model intercept plays no role, it is better is fit a linear regression model without intercept).
Variable1
Variable 2
20.00
2.00
60.00
4.00
46.00
3.00
41.00
2.00
12.00
1.00
137.00
10.00
68.00
5.00
89.00
5.00
4.00
1.00
32.00
2.00
144.00
9.00
156.00
10.00
93.00
6.00
36.00
3.00
72.00
4.00
100.00
8.00
105.00
7.00
131.00
8.00
127.00
10.00
57.00
4.00
66.00
5.00
101.00
7.00
109.00
7.00
74.00
5.00
134.00
9.00
112.00
7.00
18.00
2.00
73.00
5.00
111.00
7.00
96.00
6.00
123.00
8.00
90.00
5.00
20.00
2.00
28.00
2.00
3.00
1.00
57.00
4.00
86.00
5.00
132.00
9.00
112.00
7.00
27.00
1.00
131.00
9.00
34.00
2.00
27.00
2.00
61.00
4.00
77.00
5.00
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