Question

A pediatrician wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least-squares regression line to the data with X as the explanatory variable and Y as the response variable. He computes the following quantities: r = correlation between X and Y= 0.84 x = mean of the values of X = 5.69 y = mean of the values of Y = 6.26 S_x = standard deviation of the values of X = 3.23 s_y = standard deviation of the values of Y = 2.04 The slope of the least-squares line is: A) 0.53.B) 0.64. C) 0.84. D) 2.04.

Answer 1

Answer:

Answer is option a ) 0.53

Step-by-step explanation:

slope = $r*\frac{s_y}{s_x}$

Given that a pediatrician wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least-squares regression line to the data with X as the explanatory variable and Y as the response variable.

He finds  the following quantities:

r = correlation between X and Y= 0.84

x = mean of the values of X = 5.69

y = mean of the values of Y = 6.26

S_x = standard deviation of the values of X = 3.23

s_y = standard deviation of the values of Y = 2.04

Using the formula for slope given above substitute to get

$slope = 0.84*\frac{2.04}{3.23} \\=0.5305$

round off to 0.53

Answer is option a ) 0.53