linear regression

Question 1

what is a regression line?

Answer 1

the best line of best fit

Question 2

what is the least squares regression line?

Question 3

what are these regression lines used for?
1. y on x
2. x on y

Answer 3

1. y on x used for finding the y value given an x value
2. x on y is used for finding the x value given the y value

Question 4

what is the formula for the least squares regression line?
* y on x

Answer 4

y = a+bx

Question 5

what is the formula for the least squares rgression line
* x on y

Answer 5

x= a+ by

Question 6

in the case of a random and non random variable which least squares regression line formula would we use?

Answer 6

• y on x

Question 7

in the case of a random on random variable which least squares regression line fomrula would we use?

Answer 7

• both y on x and x on y
• 2 possible regression lines

Question 8

what is extrapolation and interpolation?

Answer 8

• interpolation: within range of given x values (more reliable)
• extrapolation: outside range of given data points (less reliable coz data may change shape )

Question 9

what are residuals?

Answer 9

on scatter graphs, the vertical distance of the point from th regression line

Question 10

what is the formula for residuals?

Answer 10

Question 11

what does the sum of square of the residuals indicate?

Answer 11

• measures how close the points rae to the regrssion line
• regression lines aims to minimise the sum of the square of the residuals

Question 12

what is the coefficent determination?

Answer 12

• square of PMCC
• determines how well the regression line is a goodness of fit

Question 13

Answer 13

Question 15

Answer 15