- Download the worksheet to save time writing
- Start solving the practice problems
- If you're stuck, watch the video solutions
- See your summary to get more insights

A retail company's year-end share price (in units of dollars) is modeled by , where is total assets (in units of billions of dollars) and is liabilities (in units of billions of dollars). Predict the share price when and .
A researcher studying the relationship between hours spent practicing piano and performance score on a music exam found the regression line . Predict the performance score for a student who practiced for hours.
What is the main goal of the least squares method in linear regression?
A researcher uses the regression equation to predict the number of hours studied () based on the number of classes attended (). The standard error of the estimate is , the mean number of classes attended is , , and . Construct a prediction interval for a student who attended classes.
A behavioral scientist examines whether there is a linear relationship between weekly meditation minutes and perceived stress score in a sample of participants. The test of the population correlation produced a -value of . State the conclusion for the hypotheses at the significance level.
Which of the following residual patterns suggests that the regression model is NOT valid?
In a study examining the relationship between study hours and test scores, a linear regression line was fitted to the data. One student studied for hours and scored , while the average test score of all students was . Which of the following best describes the total variation for this student?
The table shows the average vehicle age (in years) for each of the eight years. A regression model has been fit to the data:
Using this regression model and the actual data, compute the standard error of estimate , which measures the typical distance between observed and predicted values.
If a residual plot displays a clear curved pattern, what does this indicate about the suitability of a linear regression model?
Suppose the linear correlation coefficient for a dataset is . What is the coefficient of determination, ? Interpret the result.
Suppose the correlation coefficient for a set of data is . What is the coefficient of determination? How much of the variation is explained and how much is unexplained?
Why is R squared always non-negative, even if r is negative?
A regression model for predicting monthly sales from number of employees yields R squared = 0.05. What does this suggest?
Using the regression equation to predict the number of visitors at a museum based on advertising dollars spent (in units of thousands), find the prediction interval for if , , , and . Use the appropriate value for degrees of freedom.
A random sample of male engineering students is obtained, and their heights are measured in and in .
From the regression analysis, the predicted height in for a student who is tall is found to be . The sum of squared residuals from the regression is .
i. What is the value of the standard error of estimate (SE)?
ii. For a student whose height is , what is the prediction interval?