Points earned on a biology exam and hours spent studying for the exam were recorded for a random sample of college students. This data is presented in the scatterplot below. The correlation (or r) between points earned and hours spent studying for this sample of data is equal to 0.84, and the regression equation to predict points earned based on hours spent studying is given below:

Predicted points earned = 38.60 + 2.70 (hours studied)

Based on this information, which one of the following statements is correct?

Question

Points earned on a biology exam and hours spent studying for the exam were recorded for a random sample of college students.  This data is presented in the scatterplot below.  The correlation (or r) between points earned and hours spent studying for this sample of data is equal to 0.84, and the regression equation to predict points earned based on hours spent studying is given below:

Predicted points earned = 38.60 + 2.70 (hours studied)

Based on this information, which one of the following statements is correct?

BlackTom AI · Accepted Answer

As we analyze the statements, we proceed option by option to understand why each is true or false before identifying the correct one.
Option 1: 'The correlation coefficient should have the units of “hours per point.”' Correlation (r) is a dimensionless measure that describes the strength and direction of a linear relationship, and it does not carry units. Therefore this statement is incorrect because r has no units.
Option 2: 'If time spent studying for the exam was measured in minutes instead of hours, the value of r would not change.' Correlation is scale-invariant with respect to linear transformations like multiplying by a constant. Converting hours to minutes multiplies by 60, which affects the slope and intercept of the regression line but leaves r unchanged. Hence this statement is correct.
Option 3: 'If we decide to predict hours spent studying for the exam based on points earned on the exam, the value of r would change.' The correlation coefficient is symmetric and does not depend on which variable is predictor vs. response in terms of its numerical value. Swapping variables does not alter r. Therefore this statement is false.
Option 4: 'A student who studies for 0 hours is predicted to earn an exam score of 20 points.' Using the regression equation, predicted score = 38.60 + 2.70*(0) = 38.60, not 20. This makes the statement incorrect since it miscomputes the intercept effect.
Option 5: 'None of the above statements are correct.' Since Option 2 is correct, this option is false.
Overall, the statement that remains true is Option 2, while the others contain factual or conceptual errors related to units, symmetry of r, and the regression intercept calculation.

类似问题

A researcher collected two datasets. In Dataset A, the correlation between two measures was .60. In Dataset B, the correlation between two different measures was .30. Using this information, what can we conclude about the regression slopes in each dataset?

位置1的问题 Consider two variables, X and Y. The sign of the correlation coefficient describing the linear relationsip between X and Y has the same sign as the corresponding simple linear regression coefficient.TrueFalseDon't Know清除选择

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