Researchers wondered whether the size of a person's brain was related to the individual's mental capacity. They selected a sample of 5 females and 5 males and measured their MRI counts and IQ scores. The data is reported to the right. Complete parts (a) through (d) below.

Females Males
MRI IQ MRI IQ
816,932 133 1,001,121 140
833,868 132 1,038,436 139
856,472 140 1,079,550 141
866,662 130 924,059 136
948,066 133 955,033 139

(a) Draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable.

(b) Compute the linear correlation coefficient between MRI count and IQ. Are MRI count and IQ linearly related? Select the correct choice below and, if necessary, fill in the answe box to complete your choice.

A. No, MRI count and IQ are not linearly related since the linear correlation coefficient is .

B. Yes, MRI count and IQ are linearly related since the linear correlation coefficient is .

Step-by-step explanation:

Given that researchers wondered whether the size of a person's brain was related to the individual's mental capacity

They selected a sample of 5 females and 5 males and measured their MRI counts and IQ scores.

The data is reported to the right. Complete parts (a) through (d) below.

We want scatter plot for IQ vs MRI in general.

So we group data into two columns X for MRI and Y for IQ and draw scatter plot

MRIIQ

816932133

1001121140

833868132

856472140

866662130

1038436139

1079550141

924059136

a) Scatter plot is attached as a file

b) correlation coefficient = Cov (x,y)/S_x S_y = 0.729889

B) Yes, MRI count and IQ are linearly related since the linear correlation coefficient is .0.729889 >0.5 and near to 1 than to 0

There is a positive moderate correlation between x and y (linear)

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0