12. Regression

Linear Regression & Least Squares Method

12. Regression

Linear Regression & Least Squares Method

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Multiple Choice

The scatterplot below shows a set of data and its least-squares regression line. Based on the graph, which of the following is most likely the equation of the regression line?

$\hat{y} = 4.1 x + 50.9$

$\hat{y} = - 10.2 x + 50.9$

$\hat{y} = - 4.1 x + 50.9$

$\hat{y} = - 4.1 x - 50.9$

Verified step by step guidance

Step 1: Observe the scatterplot and the regression line. The regression line has a negative slope, as it decreases from left to right. This indicates that the coefficient of x in the equation must be negative.

Step 2: Identify the y-intercept of the regression line. The line crosses the y-axis at approximately 50, which suggests the constant term in the equation is close to 50.9.

Step 3: Compare the slope visually. The slope of the line appears to be steep, suggesting a larger absolute value for the slope coefficient. Among the options provided, the slope of -4.1 matches the visual steepness.

Step 4: Eliminate incorrect options. Based on the negative slope and the y-intercept near 50.9, eliminate equations with positive slopes or incorrect intercepts.

Step 5: Select the equation that matches both the slope and y-intercept. The correct equation is ŷ = -4.1x + 50.9.

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