Suppose the correlation between two variables (x, y) in a data set is determined to be r = 0.63, What must be true about the slope, b, of the least-squares line estimated for the same set of data? The slope will have the same sign as the correlation. The slope will have the opposite sign as the correlation. The slope will also be a value between −1 and 1. The slope b is always equal to the square of the correlation r

What can we say about the relationship between the correlation r and the slope b of the least-squares line for the same set of data? Both r and b always have values between −1 and 1. b is always larger than r. r is always larger than b. r and b have the same sign (+ or −). The slope b is always equal to the square of the correlation r.

What do all the least-squares fit lines have in common?When r = 0, there is no correlation in the data. This means that the value of y doesnot seem to be at all related to the value of x

We first introduce the concept of correlation in the Section 2.5 notes.Consider a linear model of the relationship between two quantitative variables in which the slope coefficient is non-zero. Which of the following statements about the slope coefficient and the correlation r between the two variables is correct?Question 1Select one:a.The slope coefficient could be negative when the correlation coefficient is positiveb.The slope coefficient and the correlation coefficient should have the same sign (both positive, or both negative)c.The slope coefficient could be positive when the correlation coefficient is negatived.The correlation coefficient can only be a positive value (regardless of whether the slope is positive or negative)Clear my choice

The two regression lines become identical if the correlation coefficient is

For a set of data, x is the explanatory variable. Its mean is 8.2, and its standard deviation is 1.92. For the same set of data, y is the response variable. Its mean is 13.8, and its standard deviation is 3.03. The correlation was found to be 0.223.Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place.Slope = 0.35y-intercept = 10.93Slope = 0.14y-intercept = 6.27Slope = 0.35y-intercept = 3.37Slope = 0.14y-intercept = 12.65