Simple Linear Regression

Question 1

used to show or predict the relationship (not cause-and-effect) between two variables

Answer 1

Linear regression

Question 2

predicted dependent variable

Answer 2

factor (Y)

Question 3

the independent variable used to predict the value of the Y

Answer 3

factor (X)

Question 4

finds the straight line, called the least-squares regression line

Answer 4

Linear Regression Equation

Question 5

Y = a + bX or Y = Β0 + Β1X

Answer 5

i. Y – dependent variable (goes on the Y axis)
ii. X – independent variable (plotted on the X axis)
iii. a – or B0 (regression constant) or y intercept. Eq. a = 𝑦̅ - b𝑥̅
iv. b – or B1 (regression coefficient) or slope. Eq. b = r (SY/SX)

Question 6

Assumptions for Linear Regression

Answer 6

a. Both the independent and dependent variable should be in scale.
b. There needs to be a linear relationship between the two variables
c. The dataset should be normally distributed with no significant outliers.
d. The observations must be independent
e. Data needs to show homoscedasticity

Question 7

The variances along the line of best fit remain similar as you move along the line. Residual errors are the same across all values of the predictor (or normally distributed)

Answer 7

Homoscedasticity

Question 8

the variances are not the same across all values of the predictor.

Answer 8

Heteroscedasticity

Question 9

refers to the proportion of the variance in the dependent variable that is predictable from the independent variable

Answer 9

coefficient of determination (R2)

Question 10

An R2 of 0

Answer 10

dependent variable can’t be predicted from the independent variable dependent variable can’t be predicted from the independent variable

Question 11

R2 of 1

Answer 11

dependent variable can be predicted without error from the independent variable.

Question 12

R2 between 0 and 1

Answer 12

indicates the extent to which the dependent variable is predictable