Suppose you have a data table showing the relationship between hours studied and exam scores. After calculating the regression line, how would you use a regression calculator to make a reasonable prediction for a student who studied $5$ hours?

• A. Select the highest exam score from the data table and use it as the prediction for $5$ hours studied.
• B. Find the average of all exam scores in the data table and use that as the predicted score for $5$ hours studied.
• C. Input $5$ as the value for hours studied into the regression calculator, and use the resulting predicted exam score from the regression equation as your estimate.
• D. Use the regression calculator to find the correlation coefficient and report it as the predicted exam score for $5$ hours studied.

Answer: (C)

Verified step by step guidance

1. Understand that the regression line represents the relationship between the independent variable (hours studied) and the dependent variable (exam scores). The regression equation typically has the form \(\hat{y} = b_0 + b_1 x\), where \(\hat{y}\) is the predicted exam score, \(b_0\) is the intercept, \(b_1\) is the slope, and \(x\) is the number of hours studied.
2. Use the regression calculator to input the value of hours studied, which in this case is 5. This means substituting \(x = 5\) into the regression equation.
3. Calculate the predicted exam score by evaluating the regression equation at \(x = 5\), i.e., compute \(\hat{y} = b_0 + b_1 \times 5\) using the coefficients obtained from the regression analysis.
4. Interpret the predicted value \(\hat{y}\) as the estimated exam score for a student who studied 5 hours, based on the linear relationship modeled by the regression line.
5. Avoid using unrelated statistics such as the highest exam score, the average exam score, or the correlation coefficient as predictions; the regression equation provides the most reasonable estimate for the given input.