Lecture 8C: Simple Linear Regression

Question 1

What is the main objective of simple linear regression analysis?

Answer 1

To predict the value of one variable (dependent) from another variable (independent) and determine if the prediction is statistically significant.

Question 2

What are the two variables involved in simple linear regression?

Answer 2

• Independent variable (predictor): X (usually continuous data)
• Dependent variable: Y (must be continuous data)

Question 3

In simple linear regression, what does the regression line allow you to do?

Answer 3

Predict Y from knowing the value of X.

Question 4

What is the regression equation for simple linear regression?

Answer 4

Y = bX + c

Question 5

What does ‘c’ represent in the regression equation Y = bX + c?

Answer 5

c = y-intercept (the value of Y when X=0)

Question 6

What does ‘b’ represent in the regression equation Y = bX + c?

Answer 6

b = slope of the line (unstandardized regression coefficient)

Question 7

What is the significance of R² in regression analysis?

Answer 7

R² indicates how much variance in Y can be predicted by the variance in X.

To what extent can X predict Y?

Question 8

What does an R² value of 0.123 imply in a regression model?

Answer 8

12.3% of variance in the dependent variable can be explained by the independent variable.

Question 9

What does the Adjusted R² account for in regression analysis?

Answer 9

Adjusted R² adjusts R² to remove bias, especially when the ratio of the number of predictors to sample size increases

Question 10

What does the ANOVA test determine in the context of regression analysis?

Answer 10

Whether the regression model is a significant prediction model.

Question 11

What does the term ‘coefficients’ refer to in regression analysis?

Answer 11

Coefficients indicate the relationship between the independent variable and the dependent variable.

Question 12

What does it mean if quads strength accounts for only 10.8% of the variance in 6MW distance?

Answer 12

89.2% of the variance remains unexplained by this model.

Question 13

Fill in the blank: Simple linear regression involves _______ predictor.

Answer 13

1

Question 14

True or False: Correlation is perfect in almost all cases.

Answer 14

False

Question 15

What is the purpose of running descriptive statistics before inferential statistics?

Answer 15

To check criteria and understand the basic characteristics of the data.