Reading 7: Introduction to Linear Regression

In a simple linear regression model, the variable that serves as the predictor is best described as the:

Which of the following best describes the method of Ordinary Least Squares (OLS)?

If the covariance between variables X and Y is 20 and the variance of X is 10, what is the estimated slope coefficient for the regression of Y on X?

Given a regression equation Y = 0.5 + 1.2X, how is the slope coefficient interpreted?

Calculate the intercept of a regression line where the mean of Y is 15, the mean of X is 5, and the estimated slope coefficient is 2.

Which of the following is NOT a necessary assumption of simple linear regression?

The condition where the variance of the error term is not constant across all observations is known as:

In the context of regression analysis, the term 'residuals' refers to:

If the Regression Sum of Squares (RSS) is 60 and the Sum of Squared Errors (SSE) is 40, what is the Total Sum of Squares (SST)?

The coefficient of determination (R-squared) measures:

If a regression model has an RSS of 45 and an SST of 100, what is the value of R-squared?

The Standard Error of Estimate (SEE) is calculated as the square root of which value?

In a simple linear regression with 32 observations, what are the degrees of freedom for the error term?

Calculate the F-statistic if the Mean Regression Sum of Squares (MSR) is 100 and the Mean Squared Error (MSE) is 20.

In a simple linear regression, the F-test is equivalent to determining the statistical significance of:

The appropriate degrees of freedom for the numerator in the F-test for a simple linear regression is:

If the calculated t-statistic for a slope coefficient is 2.5 and the critical t-value is 2.0, what is the appropriate conclusion?

For a simple linear regression, the null hypothesis used to test the statistical significance of the slope coefficient is:

If the standard error of the slope coefficient is 0.5 and the estimated slope is 1.5, what is the calculated t-statistic for testing if the slope is zero?

Given a regression equation Y = 2 + 3X, what is the predicted value of Y when X is 4?

In a log-lin model where ln(Y) = b0 + b1*X, how is the slope coefficient (b1) interpreted?

In a lin-log model where Y = b0 + b1*ln(X), the slope coefficient indicates:

Which functional form involves taking the natural logarithm of both the dependent and independent variables?

If a stock's return is explained by the market return, the stock's return is the:

If the correlation coefficient between two variables is 0.7, what is the coefficient of determination (R-squared)?

What is the relationship between Total Sum of Squares (SST), Regression Sum of Squares (RSS), and Sum of Squared Errors (SSE)?

In an ANOVA table, the Mean Squared Error (MSE) is calculated by dividing:

A residual plot that shows residuals increasing in magnitude as the independent variable increases indicates:

If the confidence interval for a slope coefficient includes zero, we can conclude that:

Which of the following values can the coefficient of determination (R-squared) NOT take?

Standard Error of Estimate (SEE) measures:

If a regression has an SSE of 200 and n = 22, what is the MSE?

In simple linear regression, the F-statistic is always a:

The intercept term in a regression is best interpreted as:

Using a 5 percent significance level with 34 degrees of freedom, the critical t-value is approximately 2.03. If the calculated t-statistic is 2.46, you should:

Which of the following indicates a stronger linear relationship?

If a regression has R-squared of 0.64, what is the correlation coefficient?

The Sum of Squared Errors (SSE) measures:

A confidence interval for a predicted Y-value relies on:

In a regression model Y = b0 + b1*X + error, the term 'error' represents:

If a slope coefficient is 0.64, it implies that:

In the context of the F-test, Mean Regression Sum of Squares (MSR) is calculated as:

If the correlation between X and Y is negative, the slope coefficient of the regression of Y on X must be:

A confidence interval for the predicted value of Y becomes wider when:

Which assumption is violated if the variance of the residuals increases as the predicted values increase?

Calculate the t-statistic for a slope of 1.2 with a standard error of 0.4.

In the ANOVA table for simple regression, the Total Sum of Squares (SST) degrees of freedom is:

If RSS = 80 and SSE = 20, what is the value of R-squared?

Prediction intervals are generally wider than confidence intervals because:

If a company uses a regression model to predict sales based on advertising spend, 'Sales' is the: