9.5 Making Predictions with a Regression Model

• In the equation $\text{Test Score} =$$50 +$$5 \times \text{Study Hours}$, the base score is 50.


  True
• The variable manipulated to predict changes in the dependent variable is called the independent variable.
• In the equation $\text{Test Score} =$$50 +$$5 \times \text{Study Hours}$, the y-intercept is 50
• The slope in a regression equation indicates the change in the dependent variable for a 1-unit change in the independent variable.


  True
• The y-intercept represents the predicted value of the dependent variable when the independent variable is 0.


  True
• How are predictions made using a regression model?

  By plugging values into the equation
• What is the purpose of regression models in prediction?

  To estimate outcomes
• The dependent variable is the outcome being measured or predicted.
• What is the slope in the regression equation: Test Score = 50 + 5 × Study Hours?

  5
• Substituting the independent variable into the regression equation calculates the dependent variable prediction.


  True
• The y-intercept represents the predicted value of the dependent variable when the independent variable is 0
• To make predictions using a regression model, specific values of the independent variable are plugged into the equation
• What does the slope in a regression equation represent?

  Change in dependent variable
• For each additional hour of study, the test score increases by 5 points in the equation "Test Score = 50 + 5 * Study Hours."


  True
• The y-intercept in a regression equation is the predicted value of the dependent variable when the independent variable is zero.


  True
• What is the goal of residual analysis in evaluating a regression model?

  Check for patterns
• A higher R-squared value indicates a better fit of the model to the data
• The constant variance assumption in linear regression requires the variance of residuals to be constant
• Steps to address limitations of linear regression

  1️⃣ Check model assumptions

  2️⃣ Improve model fit

  3️⃣ Evaluate prediction accuracy

  4️⃣ Consider alternative models
• What is the primary purpose of regression models?

  To predict dependent variable
• The dependent variable is measured to observe changes influenced by the independent variable.


  True
• Match the variable type with its role in prediction:

  Independent Variable ↔️ Predictor

  Dependent Variable ↔️ Outcome
• The regression equation represents the statistical relationship between the independent variable and the dependent variable.
• In the equation 'Test Score = 50 + 5 × Study Hours', the test score increases by 5 points for each additional hour of study.
• If a student studies for 2 hours, the predicted test score is 60 points.
• If a student studies for 0 hours, the predicted test score is 50 points.
• In the regression equation 'Test Score = 50 + 5 × Study Hours', the y-intercept is 50.


  True
• If a student studies for 0 hours, the predicted test score using the equation Test Score = 50 + 5 × Study Hours is 50
• Match the component of the regression equation with its definition:

  Slope ↔️ Change in dependent variable for a 1-unit change in independent variable

  Y-intercept ↔️ Predicted value of dependent variable when independent variable is 0
• What does the y-intercept of 50 in the equation Test Score = 50 + 5 × Study Hours represent?

  Base score when study hours are 0
• What is the definition of the slope in a regression equation?

  Change in dependent variable
• The y-intercept in a regression equation represents the predicted value of the dependent variable when the independent variable is zero
• To make predictions using a regression model, you must plug specific values of the independent
• In the regression equation "Test Score = 50 + 5 * Study Hours," what does the 5 represent?

  Slope
• Non-random patterns in residuals indicate model inadequacy.

  True
• What is the first step in residual analysis?

  Calculate residuals
• What is the independence assumption in linear regression concerned with?

  Independence of residuals
• What type of regression model is suitable for non-linear relationships?

  Polynomial regression
• In the equation \text{Test Score} = 50 + 5 \times \text{Study Hours}</latex>, the slope is 5
• What does the slope in the equation $\text{Test Score} =$$50 +$$5 \times \text{Study Hours}$ indicate?


  Change in test score per study hour