1. In the study of linear regression analysis, distinguish between the following expressions: (a) regressand and regressor (b) predicand and predictor (c) simple and multiple regression models

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BMS 2323 & 2326: BUSINESS STATISCS II
1. In the study of linear regression analysis, distinguish between the following expressions:
(a) regressand and regressor
(b) predicand and predictor
(c) simple and multiple regression models
2. Consider the following table:
X
3
2
2
3
6
6
3
7
4
3
8
Y
|25 15
9
28
65
60
30
80
35
32
85
70
(a) Fit the regression model
Y, = B, + B, X , + u,
(b) Determine the coefficient of determination and interpret it.
(c) Test the hypothesis : H: B =0 versus H, : B, +0 at 5% level of significance.
(d) Find the 90 % confidence interval of the expected mean prediction for x = 6.
CAT 2
1. Use the table below:
X1
15
20
25
30
35
40
45
48
50
60
X2
100
110
115
120
140
142
144
146
150
160
1
3
3
3
4
5
6
(i) Fit a regression equation to the multiple regression model
Y = B, + B, × ,
+ B, X i2
+u,
by least squares method.
(ii) Predict Y when X1=3.5 and X2=5.5
(iii) Compute TSS, ESS and RSS.
(iv) Test for the significance of overall regression at 5% level of significance.
Transcribed Image Text:BMS 2323 & 2326: BUSINESS STATISCS II 1. In the study of linear regression analysis, distinguish between the following expressions: (a) regressand and regressor (b) predicand and predictor (c) simple and multiple regression models 2. Consider the following table: X 3 2 2 3 6 6 3 7 4 3 8 Y |25 15 9 28 65 60 30 80 35 32 85 70 (a) Fit the regression model Y, = B, + B, X , + u, (b) Determine the coefficient of determination and interpret it. (c) Test the hypothesis : H: B =0 versus H, : B, +0 at 5% level of significance. (d) Find the 90 % confidence interval of the expected mean prediction for x = 6. CAT 2 1. Use the table below: X1 15 20 25 30 35 40 45 48 50 60 X2 100 110 115 120 140 142 144 146 150 160 1 3 3 3 4 5 6 (i) Fit a regression equation to the multiple regression model Y = B, + B, × , + B, X i2 +u, by least squares method. (ii) Predict Y when X1=3.5 and X2=5.5 (iii) Compute TSS, ESS and RSS. (iv) Test for the significance of overall regression at 5% level of significance.
(iii) Compute TSS, ESS and RSS.
(iv) Test for the significance of overall regression at 5% level of significance.
2. (a) The following is a two-parameter gamma density function:
f(х;а, В) —
T(a)
where
a >0, B >0, x20.
Determine expressions in terms of a and B for (i) E[X] (ii) Var(X)
(b) Research conducted on the cleanliness of home environments and children yielded the
following data in the table below :
Condition of home
Clean
Dirty
Condition of child
Clean
72
48
Fairly clean
78
22
Dirty
35
45
(i) Calculate expected frequencies for the various cells.
(ii) Test the hypothesis that there is a gap between the two conditions of cleanliness at 5%
level
of significance.
END
Transcribed Image Text:(iii) Compute TSS, ESS and RSS. (iv) Test for the significance of overall regression at 5% level of significance. 2. (a) The following is a two-parameter gamma density function: f(х;а, В) — T(a) where a >0, B >0, x20. Determine expressions in terms of a and B for (i) E[X] (ii) Var(X) (b) Research conducted on the cleanliness of home environments and children yielded the following data in the table below : Condition of home Clean Dirty Condition of child Clean 72 48 Fairly clean 78 22 Dirty 35 45 (i) Calculate expected frequencies for the various cells. (ii) Test the hypothesis that there is a gap between the two conditions of cleanliness at 5% level of significance. END
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