Question 2 a consider the data below over the relationship...

QUESTION 2 (a) Consider the Data below over the relationship between x and y X Y 2 2 1 3 4 5 7 6 8 7 10 10 4 12 (i) Find the appropriate least square regression equation. [8 marks] (ii) From the equation, Find x when y = 6 [2 marks] ii) Calculate the correlation coefficient (r) by product moment formula [8 marks] (iv) Find correlation coefficient of determination [2 marks]

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 In this question here, in a part we have given data that is x, y, xy, x square and y square.

00:10 So that is 2, 1, 4, 7, 8, here 2, xy is 4, x square is also 4 and y square is 4.

00:23 Y is given 3, 5, 6, 7, so for here xy is 3, x square is 1 and y square is 9.

00:37 Here xy is 20, x square is 16 and y square is 25.

00:45 Here xy is 42, x square is 49 and y square is 36.

00:54 Here xy is 56, x square is 64 and y square is 49, 10 and 4.

01:05 So here y is given 10, 12, so for here xy is 100, x square is 100 and y square is also 100 and here xy is 48, 16, y square is 144.

01:19 So here, here getting total of all, it comes 36, 45, 273, 250 and 367.

01:35 So, let's see first part.

01:38 So here, appropriate least square regression equation is appropriate least square regression equation is sigma y equals to a1 sigma x plus a0 n.

02:10 So, sigma y is 45 equals to 36 a1 plus 7 a0.

02:18 So, this is our first equation.

02:20 Now, sigma xy equals to a1 sigma x square plus a0 sigma x.

02:28 So, here sigma xy is 273 equals to 250 a1 plus 36 a0.

02:38 So, this is our second equation.

02:40 Now, solving, solving first and second equation, we get a0 equals to 711 divided by 227.

02:54 So, it will come 3 .132 and a1 equals to 291 divided by 454.

03:05 So, when we calculate it, we get 0 .641...