Question

Using the computer output, what is the equation of the least-squares regression line? The scatterplot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters.

a) y = 4.317 + 0.310x
b) y = 0.310 + 4.317x
c) y = -14.71 + 1.585x
d) y = 1.585 - 14.71x

Answer 1

The correct equation of the least-squares regression line is y = 4.317 + 0.310x, which suggests the starting value of y is 4.317, and it increases by 0.310 for each additional centimeter of handspan.

Step-by-step explanation:

The equation of the least-squares regression line is used to predict the value of a dependent variable based on the value of an independent variable.

In the context of the student's question, where the number of pretzels that can be grabbed is correlated with handspan, the correct equation from the given options would be the one that follows the formula y = a + bx, where a is the y-intercept and b is the slope of the line.

Referencing the general format for a regression line, y = a + bx, and looking at the provided options, the correct answer would be option (a): y = 4.317 + 0.310x. This equation suggests that the intercept (starting value of y when x is zero) is 4.317 and for every 1 cm increase in handspan, the number of pretzels students can grab increases by 0.310. The correct option is a.