Chapter 9 simple linear regression/correlation slide 13 onwards

Question 1

3 assumptions when doing pearson correlation analysis

Answer 1

• X and Y are quantitative data
• Variables X and Y are simple random variables
• Pairs of X and Y follow the bivariate normal distribution
  
  • individual variables are normally distributed
  • r is sensitive to outliers

Question 2

Strong positive relationship correlation coefficient

Answer 2

Close to +1

Question 3

Negative linear relationship correlation coefficient

Answer 3

Close to -1

Question 4

No linear relationship correlation coefficient

Answer 4

Close to zero

Question 5

Hypothesis testing for correlation

Answer 5

ρ (represents correlation coefficient of populations)
Null hypothesis: ρ =0
Alternative hypothesis: ρ not equals to zero

Question 6

Often, coefficient of determination is expressed as

Answer 6

Proportion or percentage

Question 7

What does it mean when coefficient of determination r^2 is 0.85

Answer 7

85% of the change in y is caused by a change in x

Question 8

The ______ the correlation coefficient, the ______ the coefficient of determination. This implies that _________ in dependent variable is influenced by independent variable

Answer 8

larger, larger, more changes

Question 9

interpretation when r^2 is zero

Answer 9

no correlation

Question 10

interpretation when r^2 is up to 49%

Answer 10

low correlation (need consider e sign)

Question 11

interpretation when r^2 is 50-95%

Answer 11

high correlation, need to consider the sign

Question 12

interpretation when r^2 is 96-99%

Answer 12

very high correlation, need to consider the sign

Question 13

interpretation when r^2 is 100

Answer 13

perfect correlation (need to consider the sign)

Question 14

2 methods for determining correlation for non-normally distributed data

Answer 14

logarithmic transformation and non-parametric correlation analysis

Question 15

what is non-parametric correlation analysis

Answer 15

ranking data from smallest to largest using Kendall’s or Spearman’s rank correlation to calculate the correlation coefficient

Question 16

5 properties of simple linear regression

Answer 16

• relationship between 2 variables is approx best fit line or straight line
• one independent and one dependent variable
• aka regression analysis
• forms a simple equation to describe relationship
• intercept: alpha, slope: beta

Question 17

General equation for simple linear regression

Answer 17

y’=beta x + alpha

Question 18

What is Y-Y’

Answer 18

errors of prediction

Question 19

What is Y’

Answer 19

predicted values

Question 20

5 things needed to calculate linear regression

Answer 20

• mean of X
• mean of Y
• standard dev of X
• standard dev Y
• r (correlation between x and y)

Question 21

Formula for slope

Answer 21

r(standard dev of y)/standard dev x

Question 22

Formula for intercept

Answer 22

alpha= mean of y- beta(mean of x)

Question 23

3 potential factors that affect correlation and regression

Answer 23

Outliers, multiple observations from same subject, combine data collected from differet populations

Question 24

2 effects of outliers on regression line

Answer 24

• over influence the regression line

- increase the residual error and reducing correlation

Question 25

Outlier at high end of distribution affects the correlation coefficient _________ than outliers that do not lie at the high end of distribution

Answer 25

more

Question 26

2 methods to identify outliers

Answer 26

Examine scatter plot or examine residual plot

Question 27

Explain more about the scatter plot and how it can be used to observe outliers

Answer 27

• linear regression takes into account the points in order to derive the best fit line
• the point to the regression line is known as errors of prediction
• small value: error of prediction is small
• large value: error of prediction is large

Question 28

1 commonly used criterion for best fitting line

Answer 28

line that minimizes the sum of squared errors of prediction

Question 29

What does residual plot consist of

Answer 29

Consists of plotting the (y-y’) against x

Question 30

What is a good regression plot

Answer 30

• usually no pattern

- (y-y’) are randomly distributed and it is closer to zero (y axis)