Questions: QUESTION 6 The regression equation for predicting number of hospital visits (Y') from information about patient's age (X) is Y'= 3.12+(-0.10)(X). Approximately how many visits would you predict for a 40-year-old? (Round to the nearest whole number)

QUESTION 6 The regression equation for predicting number of hospital visits (Y') from information about patient's age (X) is Y'= 3.12+(-0.10)(X). Approximately how many visits would you predict for a 40-year-old? (Round to the nearest whole number)
Transcript text: QUESTION 6 The regression equation for predicting number of hospital visits ( $Y^{\prime}$ ) from information about patient's age $(X)$ is $Y^{\prime}=$ $3.12+(-0.10)(X)$. Approximately how many visits would you predict for a 40 -year-old? (Round to the nearest whole number)
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Solution

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Solution Steps

Step 1: Define the Regression Equation

The regression equation for predicting the number of hospital visits \( Y' \) based on the patient's age \( X \) is given by:

\[ Y' = 3.12 + (-0.10)(X) \]

Step 2: Substitute the Age

To predict the number of hospital visits for a 40-year-old patient, we substitute \( X = 40 \) into the regression equation:

\[ Y' = 3.12 + (-0.10)(40) \]

Step 3: Calculate the Predicted Visits

Now, we perform the calculation:

\[ Y' = 3.12 - 4 = -0.88 \]

Step 4: Round the Result

The predicted number of hospital visits before rounding is \( -0.88 \). Rounding this value to the nearest whole number gives:

\[ \text{Predicted visits (after rounding)} = -1 \]

Final Answer

The predicted number of hospital visits for a 40-year-old patient is \\(\boxed{-1}\\).

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