Questions: Question 10 (10 points) Based on the data from six students, the regression equation relating number of hours of preparation (x) and test score (y) is y=67.3+1.07x. What is the predicted test score for a student who spent 2 hours preparing for the test? A) 59.7 B) 78.1 C) 75.2 D) 69.4

Question 10 (10 points) Based on the data from six students, the regression equation relating number of hours of preparation (x) and test score (y) is y=67.3+1.07x. What is the predicted test score for a student who spent 2 hours preparing for the test? A) 59.7 B) 78.1 C) 75.2 D) 69.4
Transcript text: Question 10 (10 points) Listen Based on the data from six students, the regression equation relating number of hours of preparation $(x)$ and test score $(y)$ is $y=67.3+1.07 x$. What is the predicted test score for a student who spent 2 hours preparing for the test? A) 59.7 B) 78.1 C) 75.2 D) 69.4
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Solution

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Solution Steps

Step 1: Define the Regression Equation

The regression equation relating the number of hours of preparation \( (x) \) and the test score \( (y) \) is given by:

\[ y = 67.3 + 1.07x \]

Step 2: Substitute the Value of \( x \)

To find the predicted test score for a student who spent \( 2 \) hours preparing, we substitute \( x = 2 \) into the regression equation:

\[ y = 67.3 + 1.07(2) \]

Step 3: Calculate the Predicted Test Score

Now, we perform the calculation:

\[ y = 67.3 + 2.14 = 69.44 \]

Final Answer

The predicted test score for a student who spent \( 2 \) hours preparing is:

\[ \boxed{69.44} \]

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