Simple Linear Regression Lesson

Multiple Choice

Which of the following methods can be used to visually estimate the relationship between two variables?

• Scatter Plot

• Coefficient of Determination

• Least Square Method

• Coefficient Of Pearson Correlation

Multiple Choice

Which of the following best describes the difference between regression analysis and correlation analysis?

• Regression analysis investigates how two or more variables are related in the form of an equation, while correlation analysis measures the strength of the relationship between two variables.

• Regression analysis measures the strength of the relationship between two variables, while correlation analysis investigates how variables are related in the form of an equation.

• Both regression and correlation analysis only measure the strength of the relationship between variables.

• Regression analysis and correlation analysis are the same statistical methods.

Multiple Choice

In a simple linear regression, the independent variable is also called the:

• Response variable

• Dependent variable

• Outcome variable

• Explanatory variable

Multiple Select

Which of the following are characteristics of regression models?

• They use equations to set up relationships between variables.

• They are used mainly for prediction and estimation.

• They only involve categorical variables.

• They require at least one numerical dependent variable.

Fill in the Blanks

Fill in the blank: A regression model with more than one explanatory variable is called a

regression model.

Multiple Choice

In the linear equation Y = mX + b, what does the variable 'm' represent?

• Slope

• Y-intercept

• Change in Y

• Change in X

Multiple Choice

Which component in the linear regression model represents the random error?

• β₀

• β₁

• εᵢ

• Xᵢ

Fill in the Blanks

The method used to estimate the parameters of a linear regression model by minimizing the sum of squared differences between observed and predicted values is called the

method.

Multiple Choice

Which of the following statements about scatter plots is/are correct?

• The explanatory variable is plotted on the y-axis.

• The response variable is plotted on the x-axis.

• Scatter plots display paired quantitative data.

• Scatter plots are only used for categorical data.

Multiple Choice

What does a scatter plot help visualize in regression analysis?

• Sample size

• Normality of residuals

• Linear relationship between variables

• Level of statistical significance

Multiple Choice

How does changing the slope versus changing the intercept affect the position of the best fit line through a set of points?

• Changing the slope rotates the line, while changing the intercept shifts it up or down.

• Changing the intercept rotates the line, while changing the slope shifts it up or down.

• Both slope and intercept only shift the line up or down.

• Both slope and intercept only rotate the line.

Multiple Choice

Which method is used to find the best fit line in linear regression?

• Maximum likelihood

• Least absolute deviation

• Least squares method

• Correlation analysis

Fill in the Blanks

Fill in the blank: The Least Squares method minimizes the sum of the squared

between actual and predicted values.

Multiple Choice

Which of the following statements about the Least Squares method are correct?

• It minimizes the sum of the squared differences between actual and predicted Y values.

• It minimizes the sum of the absolute differences between actual and predicted Y values.

• It maximizes the sum of the squared differences between actual and predicted Y values.

• It minimizes the sum of the squared X values.

Multiple Choice

Which of the following is the correct formula for the predicted Y value (ŷᵢ) in a simple linear regression model?

• ŷᵢ = β₀ + β₁xᵢ

• ŷᵢ = β₁ + β₀xᵢ

• ŷᵢ = β₀xᵢ + β₁

• ŷᵢ = β₀ - β₁xᵢ

Multiple Choice

Which equation is used to calculate the mean square error (MSE) in linear regression analysis?

• MSE = SSE / (n - 2)

• MSE = Syy - β₁Sxy

• MSE = Sxy / Sxx

• MSE = Sxx / Sxy

Multiple Choice

What does the slope coefficient β1​ represent in a simple linear regression?

• The predicted value of y when x=0

• The strength of the correlation

• The change in y for a one-unit change in x

• The total variation in y

Multiple Choice

In hypothesis testing of β1=0, what does the null hypothesis H0:β1=0 imply?

• There is no intercept

• The slope is negative

• No linear relationship exists

• The residuals are normally distributed

Multiple Choice

What is the value range of Pearson’s correlation coefficient (r)?

• 0 to 1

• -1 to 1

• -∞ to +∞

• 0 to ∞

Multiple Choice

Which of the following is NOT true about the coefficient of determination (R²)?

• It measures how well the regression line fits the data

• It ranges from -1 to 1

• R² = 1 means perfect fit

• R² = 0 means no linear relationship

Multiple Choice

If r=0.91, what is the coefficient of determination (R²)?

• 0.91

• 0.8281

• 0.81

• 1.82

Multiple Choice

What is the main purpose of using simple linear regression in statistics?

• To estimate the relationship between two variables

• To calculate the mean of a dataset

• To determine the mode of a dataset

• To find the median of a dataset