Question

Let xi = i for i = 1, 2, . . . , 15, and let...

Let xi = i for i = 1, 2, . . . , 15, and let the corresponding yi (i = 1, 2, . . . , 15) numbers be (in the order of indeces) 5, 15, 42, 57, 65, 68, 69, 83, 87, 98, 105, 108, 108, 108, 110. Calculate the least squares regression line for these data.

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Answer #1

Ans:

x y xy x^2
1 5 5 1
2 15 30 4
3 42 126 9
4 57 228 16
5 65 325 25
6 68 408 36
7 69 483 49
8 83 664 64
9 87 783 81
10 98 980 100
11 105 1155 121
12 108 1296 144
13 108 1404 169
14 108 1512 196
15 110 1650 225
Total 120 1128 11049 1240

slope,b=(15*11049-120*1128)/(15*1240-120^2)=7.2321

y-intercept,a=(1128-7.2321*120)/15=17.343

Regression equation:

y'=7.2321x+17.343

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