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?

• A. $\hat{y}=4.1x+50.9$
• B. $\hat{y}=-10.2x+50.9$
• C. $\hat{y}=-4.1x+50.9$
• D. $\hat{y}=-4.1x-50.9$

Answer: (C)

Verified step by step guidance

1. 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.
2. 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.
3. 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.
4. 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.
5. Step 5: Select the equation that matches both the slope and y-intercept. The correct equation is ŷ = -4.1x + 50.9.