Chapter 10 - Simple Linear Regression

Question 1

State the simple linear regression model

Answer 1

Question 2

State the formula for residuals in Simple Linear Regression

Answer 2

Question 3

State the formula for sum squares of Y

Answer 3

Question 4

State the formula for the sum squares of X

Answer 4

Question 5

State the formula for the sum of squares X & Y

Answer 5

Question 6

State the formula’s to determine the Simple Linear Regresion line

Answer 6

Question 7

What is the sum squares of the residuals?

Answer 7

All the variation not explained by the model

Question 8

What is the sum square of reggresion?

Answer 8

Question 9

What is the total of sum of squarse? In simple linear regression

Answer 9

Question 10

What is SS-total equal to when there is no correlation in simple linear regresion analysis?

Answer 10

Question 11

How is an ANOVA table laid out for linear regression?

Answer 11

Question 12

State the distrubution of b1 in simple linear regression

Answer 12

s = sqr(SS-res/(n-2))

Question 13

What is the correlation coefficient?

Answer 13

Question 14

What is the r^2 ?

Answer 14

Square of the correlation coefficient, also equal to (SS-reg/SS-total)

Question 15

What are the assumptions of simple linear regression?

Answer 15

1. Linear model is appropriate
2. Error terms are normally distributed
3. error terms have constant variance
4. error terms are uncorrelated

Question 16

When r^2 = 0, what is SS-total equal to?

Answer 16

r = 0, b1 = 0, SS-reg = 0, SS-total = SS-res

Question 17

In simple linear regression, when are points considered outliers?

Answer 17

When they have a normal residual > 2 in magnitude

Question 18

In simple linear regression, how can we check that the linear model is appropriate?

Answer 18

1) scatterplot of xi & yi should show points rougly around a line
2) scatter plot of standardised residuals against fitted values should not have a pattern
3) scatter plot of standardised residuals against xi should not have a pattern

Question 19

In simple linear regression, how can we check that errors are normally distributed?

Answer 19

a) Histogram of residuals should look normal
b) Normal probability plot should have a straight line

If the data is right skewed, fix by sqr(), cubert() or log() to the y value (in increasing severity)

If the data is left skewed, fix by sqr(), cube(), exp() to the y value (in increasing severity)

Question 20

In simple linear regression, how can we check that errors have constant variance?

Answer 20

A scatterplot of standardised residuals against xi and fitted values should show constant spread.

Question 21

In simple linear regression do we check if the errors are correlated?

Answer 21

Not in this course we don’t