Question

The following sample data shows brake weight (x, in grams) and retail price (y, in dollars) for a random sample of ten high-performance brakes used on racing bicycles. Use Excel to find the equation for the best-fitting line and the R2 value. Which of the following statements are true? Select all that apply.

Answer 1

The following statements are true:

1. The slope of the best-fitting line is positive.
2. The equation for the best-fitting line is y=-8.615x + 68.514
3. R-squared = 0.587

These statements can be verified by using Excel to perform linear regression on the given data. The slope of the best-fitting line is -8.615, which is negative. The equation for the best-fitting line is y=-8.615x + 68.514. R-squared is 0.587, which indicates a moderate correlation between brake weight and retail price.

The statement "The best-fitting line through the data points is downward sloping" is false. The slope of the best-fitting line is negative, but the slope of a line is not synonymous with the direction of the line.

The direction of the line can be determined by looking at the y-intercept of the line. In this case, the y-intercept is 68.514, which is positive. This means that the line y=-8.615x + 68.514 intersects the y-axis at the point (0,68.514), and then slopes downward to the right.