Linear regression

Question 1

What is regression? how is it different from correlation?

Answer 1

Regression determines if one variable predicts/explains another variable whereas correlation tells us how strongly two variables relate to each other (strength and direction)

Question 2

What is the predictor variable?

Answer 2

• independent variable
• explanatory variable
• X variable in regression model

Question 3

What is the outcome variable?

Answer 3

• dependent
• criterion variable
• Y variable in regression model

Question 4

What is linear regression?

Answer 4

A form of regression that assesses the linear relationship between one or more (continuous or categorical) predictor variable variables and a continuous outcome variable

Question 5

What is the difference between simple linear regression and multiple linear regression?

Answer 5

Simple = one predictor and one outcome
multiple = two or more predictor and one outcome

Question 6

How would you write you hypothesis

Answer 6

H0: Self-presentation on TikTok does not significantly predict slang use intention on TikTok.
Ha: Self-presentation on TikTok significantly predicts slang use intention on TikTok (positively/negatively).

Question 7

What is the mean model? is it a good model?

Answer 7

Mean model uses the average of Y as the predictor value for all observations
- not a good model as ignores the actual y values

Question 8

What is a regression line?

Answer 8

line of best fit, pass through some of the points but not all
- does not make perfect predictions

Question 9

What is the residuals on regression line?

Answer 9

difference between what model predicted and the value of the actual model

Question 10

What do residuals help us do?

Answer 10

• measure error in the predictions
• error in regression does not = mistake
• error represents the difference between actual values and predicted values
• shows us how well model fits data

Question 11

If the actual value is above the regression line, the residual is…

Answer 11

positive

Question 12

What does it mean if there is more positive residuals or more negative?

Answer 12

pos = model underestimates
neg = model overestimates

Question 13

What is the linear regression formula?

Answer 13

y = a + bx (y = outcome variable, x = predictor variable)

Question 14

What is a in the equation (y = a + bx)

Answer 14

a is the intercept, the value of y when x = 0

Question 15

explain 𝐘̂=𝐛_𝟎+ 𝐛_𝟏 𝐗

Answer 15

Ŷ (Y hat) = The predicted outcome based on the regression model

X = The predictor variable

𝑏_0 “(beta−zero)” = the intercept, representing the predicted value of Y when X = 0

𝑏_1 (beta-one) represents the change in the predicted Y for each 1-unit increase in X

Question 16

what is b in the equation (y = a + bx)

Answer 16

the slope, tells us how much y changes when x is increased by 1

Question 17

How do we find the slope and the intercept?

Answer 17

𝑏_0= 𝑦̅ −𝑏_1∗𝑥̅ (intercept)
𝑏_1= 𝒓∗𝒔_𝒚/𝒔_𝒙 (slope)

𝑥̅ and 𝑦̅ are the mean values of X and Y
𝒓 is the Pearson correlati