Linear Regression 1

Question 1

What do correlations tell us?

Answer 1

How strongly two continuous variables covary.

Question 2

To what is correlation not equal?

Answer 2

Causation

Question 3

To what is linear regression conceptually similar?

Answer 3

Correlation

Question 4

What is the difference between correlation and linear regression?

Answer 4

Unlike linear regression, correlation does not treat the two variables that it is evaluating differently.

Question 5

Between which two variables does linear regression distinguish?

Answer 5

Independent and dependent variables.

Question 6

What do we fit to data to describe a relationship between the two variables being evaluated in line with the linear regression concept?

Answer 6

A straight line.

Question 7

What is investigated after having fit a straight line to data in order to describe a relationship between two variables (in line with the linear regression concept)?

Answer 7

How much variance is explained by the straight line fit to the data, relative to the unexplained variance.

Question 8

Which optimisation approach is widely used to find a line that best represents the relationship between two variables?

Answer 8

The method of least squares.

Question 9

How are all straight lines represented?

Answer 9

By Y = mX + c, where X is the score on the independent variable, Y is the predicted score on the dependent variable, m is the gradient of the line, and c is the intercept.

Question 10

Which aspect of the equation representing straight lines is indicative of a positive, negative, or no relationship between two variables?

Answer 10

m

Question 11

What would m = 0 indicate?

Answer 11

The absence of a relationship between two variables.

Question 12

How is m calculated?

Answer 12

From the covariance of X and Y.

Question 13

How does the m calculation differ from the correlation coefficient calculation?

Answer 13

m is standardised according to the squared deviations in X only, rather than the X and Y standard deviations multiplied.

Question 14

What is the equation for m?

Answer 14

(COVXY/ s2x) = (Σ(X-X̄)(Y-Ȳ))/ (Σ(X-X̄)2)

Question 15

With what are regression equations also written on the end?

Answer 15

An error term (+ e).

Question 16

What does an error term signify?

Answer 16

What we can’t model with a straight line.

Question 17

How is the predicted Y symbolised?

Answer 17

As Ŷ.

Question 18

Through which intercept will a regression line go?

Answer 18

Through the intercept (x = 0)(y = 0).

Question 19

Through which values will a regression line go, as well as through the intercept (x = 0)(y = 0)?

Answer 19

The means of x and y (x = X̄)(y = Ȳ).

Question 20

When do we have our straight line model?

Answer 20

Once we have calculated our parameters.

Question 21

What do we need to assess the goodness of fit of a linear regression model?

Answer 21

SST, SSR, and SSM.

Question 22

To what does SST refer?

Answer 22

To the total variability in data (the difference between each Y value and the mean Y value).

Question 23

To what does SSR refer?

Answer 23

To the differences between the observed Y values and those predicted by the model (the residual/ unexplained variance).