To predict the \( y \)-value for \( x \)-value 69 you run a regression analysis on a bivariate set of data, after checking the data points in the scatter plot had few outliers and were roughly grouped around a (straight) line. Use significance level of \( \alpha=.05 \) to assess the strength of the linear correlation. Linear Regression results are \[ \hat{y}=-0.2 x+4.1 \] You also find \( \bar{x}=10.7 \) and \( \bar{y}=2 \). To predict the \( y \)-value when \( x=69 \), \( y \approx \) \( \bar{x}=10.7 \) \( \hat{y}=-0.2 \cdot 69+4.1=-9.7 \) \( \bar{y}=2 \) All of these None of these

To predict the \( y \)-value for \( x = 69 \) using the given linear regression equation, we will follow these steps: 1. **Identify the regression equation**: The regression equation provided is \[ \hat{y} = -0.2x + 4.1 \] 2. **Substitute \( x = 69 \) into the regression equation**: \[ \hat{y} = -0.2 \cdot 69 + 4.1 \] 3. **Calculate the value**: - First, calculate \( -0.2 \cdot 69 \): \[ -0.2 \cdot 69 = -13.8 \] - Now, add \( 4.1 \): \[ \hat{y} = -13.8 + 4.1 = -9.7 \] Thus, the predicted \( y \)-value when \( x = 69 \) is: \[ \hat{y} \approx -9.7 \] Now, let's assess the strength of the linear correlation using the significance level \( \alpha = 0.05 \). However, we need additional information such as the correlation coefficient \( r \) or the \( p \)-value to make this assessment. Since this information is not provided, we cannot conclude about the strength of the linear correlation. ### Summary of Results: - The predicted \( y \)-value when \( x = 69 \) is \( -9.7 \). - The values \( \bar{x} = 10.7 \) and \( \bar{y} = 2 \) are provided but are not directly relevant to the prediction of \( y \) for \( x = 69 \). ### Final Answer: The predicted \( y \)-value when \( x = 69 \) is \( -9.7 \). So, the correct option is: - \( y \approx -9.7 \)