2.6 Linear Regression Models

• What does 'y' represent in the linear regression equation?

  Dependent variable
• The relationship between independent and dependent variables should ideally exhibit a linear trend
• What is the interpretation of the slope in the model Exam Score = 5 * Study Hours + 60?

  Each study hour increases score by 5
• What does 'y' represent in the linear regression equation?

  Dependent variable
• The slope in a linear regression model is denoted by 'm'.

  True
• What does the slope in a linear regression model represent?

  Change in y for x
• What is the general equation of a linear regression model?

  y = mx + b
• In the example "Exam Score = 5 * Study Hours + 60," Exam Score is the dependent variable
• The slope in a simple linear regression model represents the change in y for each unit increase in x
• In the example "Exam Score = 5 * Study Hours + 60," what does the y-intercept of 60 indicate?

  Score without studying
• What statistical technique is used to model the relationship between two quantitative variables by fitting a straight line to the data?

  Linear regression model
• What does the y-intercept in a linear regression model represent?

  Value of y when x is 0
• In the linear regression model "Exam Score = 5 * Study Hours + 60," the slope is 5
• An R-squared value of 1 indicates that the model explains all of the variance
• What does the y-intercept in a linear regression model indicate?

  Score without studying
• An R-squared value of 0 indicates the model explains none of the variance in the dependent variable.


  True
• A higher R-squared value indicates a better model fit.

  True
• The assumption of linearity requires a linear relationship between the dependent and independent variables.


  True
• The normality of errors is examined using a histogram of the residuals.


  True
• Match the notation with its description:

  y ↔️ Dependent variable

  x ↔️ Independent variable

  m ↔️ Slope

  b ↔️ Y-intercept
• In the model Exam Score = 5 * Study Hours + 60, the y-intercept is 60.
• What is a linear regression model used for?

  Predicting a dependent variable
• The y-intercept is the value of y when x equals 0.


  True
• What is the independent variable in the example Exam Score = 5 * Study Hours + 60?

  Study Hours
• A linear regression model is used to model the relationship between two quantitative variables
• The slope in a linear regression model measures the change in y for a unit increase in x
• In the model Exam Score = 5 * Study Hours + 60, what is the value of the slope?

  5
• The y-intercept in a linear regression model is the value of y when x is 0
• Arrange the key components of a linear regression model from general to specific.

  1️⃣ Dependent Variable (y)

  2️⃣ Independent Variable (x)

  3️⃣ Slope (m)

  4️⃣ Y-Intercept (b)
• In the example "Exam Score = 5 * Study Hours + 60," the y-intercept is 60.

  True
• Match the component with its description in a simple linear regression model:

  Dependent Variable ↔️ Variable to be predicted

  Independent Variable ↔️ Variable used for prediction

  Slope ↔️ Change in dependent variable per unit change in independent variable

  Y-Intercept ↔️ Value of dependent variable when independent variable is 0
• A linear regression model is used to fit a straight line to the data
• The general equation of a linear regression model is y = mx + b
• Match the component with its description:

  Dependent Variable ↔️ The variable to be predicted

  Independent Variable ↔️ The variable used for prediction

  Slope ↔️ Change in dependent variable per unit change in independent variable

  Y-Intercept ↔️ Value of dependent variable when independent variable is 0
• The linearity of a relationship in simple linear regression can be visually assessed using a scatterplot.


  True
• An R-squared value of 0 means the model explains none of the variance in the dependent variable.


  True
• Interpreting linear regression values helps predict the impact of the independent variable on the dependent variable.

  True
• If a linear regression model has an R-squared of 0.75, what percentage of the variation in exam scores does the model explain?

  75%
• What are the key assumptions of linear regression models?

  Linearity, independence, normality, homoscedasticity
• Which test is used to check for independence of errors in linear regression?

  Durbin-Watson test