Question

You have a set of data that you have labeled as x (explanatory) and y (response). You run summary statistics and get the following. Both variables are quantitative. Summary Statistics Column Mean Variance Std dev Std error Median Min Max 18 32.5 145.206 12.05 2.84 32.5 17 54 у 18 6.778 7.007 2.647 0.624 6.5 2 11 n Х Correlation between x and y is 0.555 What is the equation of the linear regression? Important: Round your value for the slope to three decimal places and then use that to compute the value of b. Answer: ŷ + 2 (Please show your answers to three decimal places)

Answer 1

Problem statement: We are presented with a data which provides the summary measures of explantory variable (x) and response variable (y). Based on this information we have to compute the regression cofficients to highlight the relationship between the variables.

Given: A table is provided with the summary statistics of explantory variable (x) and response variable (y). Also coefficient of correlation is provided, highlighting that there seems to be linear relationship to certain extent between the variables. Based on this information we have to build a regression model and compute the regression coefficients.

Solution: Regression model helps to obtain the linear relationship between explantory variable (x) and response variable (y) in the form of

$y=b+((c)*x)$

where,

y= response variable

b= intercept of the regression model

c= slope of the regression line

x= explanatory variable

Using summary statistics we can calculate the value of slope "c" using,

$c=r*(\sigma y/\sigma x)$

where

r= coeffiecient of corrleation

$\sigma x$ = standard deviation of x

$\sigma y$ =standard deviation of y

Inserting these values in the equation we get,

c =(0.555)*(2.647/12.05)

c =0.1219

Slope of the regression line is 0.1219, Rounding it to three decimals 0.122

Intercept, b, is given by,

Using the information from the tabel we get,

b = 6.778-(0.122*32.5)

b = 2.813

Intercept of the regresion line is 2.813.

So, the total regression line for the following data is,

y=2.813+(0.122)*x