Regression and Correlation

Question 1

What is correlation?

Answer 1

Correlation quantifies the strength of the association between two quantitative variables

Question 2

What is Pearson’s correlation coefficient a measure of?

Answer 2

The scatter underlying a linear trend between two quantitative variables

Question 3

What is linear regression?

Answer 3

It studies the linear relationship between two quantitative variables when one (dependent variable) is modelled as depending on the other (independent variable)

Question 4

A linear regression model allows predictions about the dependent variable to be made among individuals. T/F?

Answer 4

True

Question 5

Correlation models allows predictions about the dependent variable to be made among individuals. T/F?

Answer 5

False

Question 6

Correlation is quantified on a scale from -1 to 1. T/F?

Answer 6

True

Question 7

What are the assumptions in calculating correlation?

Answer 7

Independent observations
Bivariate Normal distribution
Relationship between X and Y is linear

Question 8

The value and units of measurements of variables is unimportant for measuring correlation. T/F?

Answer 8

True

Question 9

The value and units of measurements of variables is unimportant in regression models. T/F?

Answer 9

False - this is significant

Question 10

Which variable is classified as X and which as Y is significant in correlation. T/F?

Answer 10

False

Question 11

Which variable is classified as X and which as Y is significant in correlation. T/F?

Answer 11

True - Y should be the dependent variable. and X should be the independent variable

Question 12

Why is the calculation for a CI or hypothesis test for correlation not the same as for tests of associations?

Answer 12

Because the sampling variability for correlation does not follow a Normal distribution

Question 13

How can a straight line be described mathematically?

Answer 13

Y = alpha + beta X
(alpha = y-intercept)
(beta = gradient of line)

Question 14

In a regression model, what is a residual?

Answer 14

The vertical distance of a data point from the line of best fit

Question 15

How is the best fit line plotted in linear regression models?

Answer 15

The best fit line is taken as the. one which makes the sum of the squares of. the residuals as small as possible. I.e. it minimises the variance of the residuals

Question 16

What is the other name for the line of best fit in linear regression models?

Answer 16

The Least Squares Linear Regression Line

Question 17

In the Minitab/SPSS output for a linear regression model, what does the row labelled ‘constant’ represent?

Answer 17

This gives a test of the null hypothesis that the intercept of the population regression line is 0

Question 18

In the Minitab/SPSS output for a linear regression model, what does the row labelled ‘weight’ represent?

Answer 18

This gives a test of the null hypothesis that the slope of the regression line is 0

Question 19

In the Minitab/SPSS output for a linear regression model, what does the column labelled ‘SE coefficient’ represent?

Answer 19

The standard errors of the coefficients, allowing calculation of the CIs of the coefficients

Question 20

In the Minitab/SPSS output for a linear regression model, what does the quantity ‘s represent?

Answer 20

The standard deviation of the points around the regression line

Question 21

In the Minitab/SPSS output for a linear regression model, what does the row labelled ‘R-sq’ represent?

Answer 21

The coefficient of determination which tells of the percentage of the variability in Y which is explained by variation in X

Question 22

What are the assumptions for linear regression?

Answer 22

Constant variance - the spread of the response Y, about its average value is the same for all values of X
Linearity - the average of the response, Y, is a linear function of the explanatory X
Independent observations
Normality of residuals
Error free values for x - for each pair of observations, the predictor x needs to be known with no error and the response y is a random observation

Question 23

X and Y must follow a normal distribution in linear regression. T/F?

Answer 23

False

Question 24

A prediction interval (in linear regression) will be wider than the confidence interval. T/F?

Answer 24

True

Question 25

What is a prediction interval?

Answer 25

An estimate of the interval in which a future observation will fall