Linear Regression and Correlation

What is the primary purpose of linear regression analysis as described in Chapter 13?

According to Section 13.1, what does a correlation coefficient, r, measure?

In the linear equation y = a + bx, what does the constant 'a' represent?

What is the primary assumption regarding the error term (epsilon) in the Ordinary Least Squares (OLS) regression model?

If a correlation coefficient (r) is calculated to be -0.95, what does this value indicate?

What is the null hypothesis (H0) when performing a hypothesis test for the significance of a correlation coefficient?

In a simple linear regression equation y = a + bx, if the slope 'b' is 5, how should this be interpreted?

What does the term 'homoscedasticity' refer to in the context of OLS regression assumptions?

A researcher wants to estimate the elasticity of demand for a product. Which data transformation would provide a direct estimate of elasticity from the regression coefficient?

What is the main difference between a confidence interval and a prediction interval in regression analysis?

In the regression output shown in Figure 13.25 for the demand for roses, what is the estimated coefficient for the price of carnations?

What does the R Square value of 0.732792 in the regression output (Figure 13.25) signify?

Based on the regression equation derived from Figure 13.25 (Quantity of roses sold = 183,475 – 1.76 Price of roses + 1.33 Price of Carnations + 3.03 Income), what is the predicted effect of a one dollar increase in per capita income?

What is the phenomenon called when two or more independent variables in a multiple regression model are highly correlated?

Why does multicollinearity lead to frustrating results in regression analysis, according to Section 13.4?

What is the purpose of using a dummy variable in a regression model?

In the example of teacher salaries (Figure 13.14), the coefficient for the dummy variable 'Gender (man = 1)' is 632.38. How is this interpreted?

What is the key takeaway from the Gauss-Markov Theorem regarding OLS estimates?

According to the text, why must one be cautious when predicting a Y value for an X value that is outside the range of the original data?

In testing the overall quality of a multiple regression model, what does the F-test determine?

Svetlana charges a one-time fee of 25 dollars plus 15 dollars per hour for tutoring. The equation is y = 25 + 15x. What is the interpretation of the y-intercept in this context?

If the line of best fit is y-hat = 173.51 + 4.83x, what is the predicted final exam score for a student who scored 73 on the third exam?

What does a 'residual' or 'error' term represent in a regression context?

The method of determining the best-fit line is called 'least squares' analysis because it minimizes which of the following?

In a semi-log regression where the dependent variable Y is converted to log(Y), how is the coefficient 'b' of the independent variable X interpreted?

What type of data involves observing multiple units (e.g., people, companies) at a single point in time?

What does the 'Significance F' value in the ANOVA table of an Excel regression output represent?

If a simple linear regression is performed and the correlation coefficient, r, is exactly +1, what can be said about the data points?

What is a key disadvantage of using a high R-squared value as the sole measure of a regression model's quality?

In testing an individual regression coefficient (e.g., b1), what is the null hypothesis?

What is the degrees of freedom for the t-statistic when testing the significance of a correlation coefficient with a sample size of 50?

A residuals plot is created after a regression analysis. What pattern in the residuals plot would suggest that the linear model is appropriate?

What is the name for the condition when the variance of the error term is NOT constant for all values of the independent variable?

In the regression output in Figure 13.25, the t Stat for the 'Price of Roses' is approximately -5.9. What does this value represent?

If a regression model is used to predict the height of a tree (Y) from the diameter of its trunk (X), what type of data is this an example of?

What is the adjusted R Square value in the regression output from Figure 13.25?

Why is the adjusted R-squared often preferred over the regular R-squared for reporting the goodness-of-fit of a multiple regression model?

What is the purpose of an 'interaction variable' in a regression model, such as the one described in Section 13.4 with dummy variables?

In the teacher salary example (Figure 13.15), if the interaction term between gender and experience is significant and positive, what does it imply?

What does a t-statistic of 2.464901 for the 'Income (per capita)' variable in Figure 13.25 indicate?

What is the test statistic used for determining the significance of a correlation coefficient, as shown in Section 13.2?

If a regression model for sales (Y) based on advertising spending (X) yields a coefficient of determination (R-squared) of 0.49, what is the correlation coefficient (r)?

Using the quick shorthand test for correlation from Section 13.2, if you have 25 observations and a correlation coefficient of 0.35, is the correlation statistically significant at the 0.05 level?

What does the term 'BLUE' stand for in the context of the Gauss-Markov Theorem?

For the SCUBA diving data in Try It 13.5, the regression line is found. If you are asked to predict the maximum dive time for a depth of 110 feet, what is this an example of?

The regression model Y = a + b*log(X) is estimated. How would you interpret the coefficient 'b'?

If a scatter plot of two variables shows the points forming a circular or cloud-like shape with no clear direction, what would you expect the correlation coefficient 'r' to be?

The line of best fit always passes through which specific point?

In the consumption function example, if consumption (Y) is measured in dollars and income (X) is measured in dollars, what are the units of the slope coefficient b1?

What is the primary reason regression analysis is considered more valuable than correlation analysis for policy decisions?