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?

$ŷ=4.1x+50.9$

$ŷ=-10.2x+50.9$

$ŷ=-4.1x+50.9$

$ŷ=-4.1x-50.9$

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 relationship between x and y is negative.

Step 2: Recall the general form of a linear regression equation: ŷ = mx + b, where m is the slope and b is the y-intercept. A negative slope means m < 0.

Step 3: Identify the y-intercept from the graph. The regression line intersects the y-axis at approximately 50, which suggests that b = 50.9 in the equation.

Step 4: Compare the slope visually. The line decreases steeply, suggesting a slope magnitude closer to -4.1 rather than -10.2. This eliminates options with incorrect slopes.

Step 5: Based on the negative slope and the correct y-intercept, the most likely equation of the regression line is ŷ = -4.1x + 50.9.

7:01m

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