BIOMETRY

1. Example: Suppose you are given data on monthly sales, Radio and Television Advertising Expenditure
and Newspaper Advertising Expenditure in sample of 22 Cities
City Y
Sales ( $ Millions)
X1
Radio and TV
Advertising ($ 000)
X2
Newspaper Advertising
($ 000)
1 9.73 0 20
2 11.19 0 20
3 8.75 5 5
4 6.25 5 5
5 9.10 10 10
6 9.71 10 10
7 9.31 15 15
8 11.77 15 15
9 8.82 20 5
10 9.82 20 5
11 16.28 25 25
12 15.77 25 25
13 10.44 30 0
14 9.14 30 0
15 13.29 35 5
16 13.30 35 5
17 14.05 40 10
18 14.36 40 10
19 15.21 45 15
20 17.41 45 15
21 18.66 50 20
22 17.17 50 20

2. a) Fit the multiple linear regression for the above data
b) Test the hypothesis that
1 2 3: ....... pHo β β β β= = = =
c) Compute the coefficient of determination and interprete
d) Construct the 95% confident intervals for individual regression parameters
e) Test the significance of regression parameters
Outputs for the above question
Source | SS df MS Number of obs = 22
-------------+------------------------------ F( 2, 19) = 121.97
Model | 232.657595 2 116.328797 Prob > F = 0.0000
Residual | 18.1216706 19 .953772135 R-squared = 0.9277
-------------+------------------------------ Adj R-squared = 0.9201
Total | 250.779266 21 11.9418698 Root MSE = .97661
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Salary Y| Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Rad&TVadvert(X1)| .1621127 .0131906 12.29 0.000 .1345044 .189721
Newsp advert(X2)| .2488677 .0279239 8.91 0.000 .1904222 .3073132
_cons | 5.257382 .4984371 10.55 0.000 4.214141 6.300623
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