12. Regression
Linear Regression & Least Squares Method
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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?
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Verified step by step guidance1
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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