Linear Regression

Question 1

What is a correlation?

Answer 1

A measure of strength of a linear relationship, between two variables.

Question 2

What are the two key factors of Correlations?

Answer 2

1. The two variables in a correlation typically reflect numerical values
2. It is represented with positive or negative values

Question 3

What is a correlation coefficient?

Answer 3

The value that indicates the strength of the relationship between two variables.
- Falls between +1 and -1

Question 4

Linear relationships are typically represented by what?

Answer 4

Pearson’s r

Question 5

What does Pearson’s r tell us?
2 points

Answer 5

Strength and direction of the relationship between two variables.

Question 6

What does regression do?

Answer 6

Expresses the relationship in the form of an equation.
- The equation for the line of best fit
- can be used to form predictions

Question 7

How many predictor variables in ‘Simple Linear Regression’?

Answer 7

1

Question 8

How many predictor variables in ‘Multiple Linear Regression’?

Answer 8

+ 1

Question 9

What is a predictor variable?

Answer 9

The name given to an independent variable in regression analysis

Question 10

What is the equation for simple regression?

Answer 10

y = a + bx
a = intercept
b = slope

Question 11

What is meant by intercept ?

Answer 11

The point the line crosses the y axis
- y = 10 + 1x (line cross y axis at point 10)

Question 12

What is meant by slope?

Answer 12

How much y increases for every increase in x
- y = 0 + 2x (2 y-units increase per 1 x-unit)
- y = 0 - 0.5x (0.5 y-units decrease per 1 x-unit)

Question 13

How can we determine the strength of a regression fit?

Answer 13

By calculating the Sum of Squares Error.
The smaller the SSerror the stronger the regression fit.

Question 14

How do you calculate the SSerror

Answer 14

1. Calculate the deviation for each data point and square it.
2. Add up all deviations

Question 15

How do you calculate Pearson’s r

Answer 15

1. convert x + y values into z scores (equation for this)
2. multiply Z values of x by Z values of y
3. Add up the column + divide by the number of participants - 1 (equation for this)

Question 16

How do you calculate the regression slope?

Answer 16

You divide the standard deviation of y by the standard deviation of x, and multiply it by Pearson’s r.
b = r (sy/sx)

Question 17

How do you calculate the regression intercept?

Answer 17

subtract the mean of y from the slope, multiplied by the mean of x.
a = mean of y - slope * mean of x.

Question 18

What is total variance?

Answer 18

How much each data point varies from the mean

Question 19

What is Error variance?

Answer 19

how much each data point varies from the predicted value

Question 20

What is regression variance?

Answer 20

How much the predicted value varies from the mean
- more regression variance = stronger relationship

Question 21

How do you calculate total variance?

Answer 21

1. Subtract the y value from the mean
2. square the difference from the mean
3. add up all the square differences

Question 22

How do you calculate Error variance?

Answer 22

1. Input the x-values into regression equation
2. subtract the predicted score from the actual test score
3. square the predicted difference
4. add up all the squared predicted differences

Question 23

What does variance explained tell us

Answer 23

how much of the data is explained by the regression model