Question

Compute the least-squares regression line for the given data set. Use a TI-84 calculator. Round final answers to four decimal places, as needed.

x 5 7 6 2 1
y 4 3 2 5 1
Regression line equation: ŷ = _______ + _______ x.

Answer 1

Y = 2.843+ 0.037 X

Explanation:

Let the equation of the straight line to be fitted to the data , be Y = a+b X where a and b are to be evaluated. The normal equations fro determining a and b are

∑Y = na +b ∑X

∑XY = a∑X + b∑X²

We now calculate ∑X, ∑Y , ∑X², and ∑XY

X Y XY X²

5 4 20 25

7 3 21 49

6 2 12 36

2 5 10 4

1 1 1 1

21 15 64 115

Thus the normal equation becomes

5a + 21b =15

21a +115b = 64

Solving these two equations simultaneously we get

105 a + 441b = 315

105a + 575b = 320

134b= 5

b= 0.037 , a= 2.843

Hence the equation for the required straight line is

Y = 2.843+ 0.037 X