Question

Consider the paired sample {(3, 1),(3, 5),(6, 6),(6, 8),(7, 10)}. Do the following by hand (you may use a basic calculator, but not a statistical program).

(a) Find estimates βˆ 0 and βˆ 1 of the regression parameters β0 and β1.

(b) Make a rough sketch of the data and regression line.

(c) Predict the value of y when x = 5.

(d) Predict the value of y when x = 15.

(e) Which prediction (part c or d) do you trust more? Why?

(f) For the data point (3, 5), calculate the residual i .

(g) Perform a test of H0 : β1 = 0 vs HA : β1 6= 0. Use α = 0.05.

Answer 1

Here observation (3, 1) denote that x1 is 3 and y1 is 1

So here we are given with observations as follows:

x	y
3	1
3	5
6	6
6	8
7	10

A)

So here we need to find the Estimated regression equation :

Regression equation of y on x is given by:

Where:

After calculating all these qunatities in calculator we get regression equation as