For which data set is a linear regression most reasonable?
a set of nine data pairs with a correlation coefficient r = –0.4
a set of five data pairs with a correlation coefficient r = 0.3
a set of four data pairs with a correlation coefficient r = –0.8
a set of six data pairs with a correlation coefficient r = 0.6

a set of four data pairs with a correlation coefficient r = –0.8

Step-by-step explanation:

We know that the correlation tells the strength of a relationship between two variables where a strong correlation means that two or more variables have a strong reasonable relationship with each other.

For strong correlation, the value of correlation coefficient must be nearest to the absolute value of 1.

Here the nearest value of correlation coefficient is -0.8 , which is nearest to -1, Hence there is strong negative correlation among all.

Therefore,a set of four data pairs with a correlation coefficient r = –0.8 is where the linear regression model is reasonable.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!