An economic development researcher wants to understand the relationship between the average monthly expenditure on utilities for households in a particular middle-class neighborhood and each of the following household variables: family size, approximate location of the household within the neighborhood, and indication of whether those surveyed owned or rented their home, gross annual income of the first household wage earner, gross annual income of the second household wage earner (if applicable), size of the monthly home mortgage or rent payment, and the total indebtedness (excluding the value of a home mortgage) of the household.

The correlation for each pairing of variables are shown in the table below:

How would you interpret the relationship between Debt and Utilities?

a. There is a strong positive linear relationship between debt and utility payments.
b. High utility payments lead to higher debt.
c. Debt and utility payments are negatively correlated.
d. There is no relationship between these two variables.

a.There is a strong positive linear relationship between debt and utility payments.

Step-by-step explanation:

Hello!

The given table shows the calculated correlation coefficients between the variables, and you have to analyze the type of correlation between them.

The coefficient of correlation gives an idea of the degree of correlation between the variables and takes values between -1 and 1

If r = 0 then there is no linear correlation between X₁ and X₂ Graphically, the slope is cero

If r < 0 then there is a negative association between X₁ and X₂ (i.e. when one variable increases the other one decreases) In a graphic, the slope of the line is negative.

If r > 0 then there is a positive association between X₁ and X₂ (i.e. Both variables increase and decrease together)

The closer to 1 or -1 the coefficient is, the stronger the association between variables. Using the absolute value of the correlation coefficients you can compare them, the greater the value, the stronger is the association between variables.

Looking at the table the correlation coefficient for the variables "Debt" and "Utilities" is:

r= 0.778

The coefficient is positive, so you can say that there is a positive correlation between the two variables, this means, that when the variable "debt" increases, so do the variable "utilities"

Also, the value is close to 1, and as said before, the closer it is to 1, the stronger the correlation between the variables.

So you could say that there is a strong positive linear correlation between the variable's debt and utility payments.

Variable "location"

Corelation with variable "Ownership" r= -0.386

Correlation with variable "First income" r= -0.537

Correlation with variable "Second income" r= -0.508

Correlation with variable "Monthly Payment" r= -0.511

Correlation with variable "Utilities" r= -0.346

Correlation with variable "Debt" r= -0.461

All correlation coefficients are negative, so all variables have a negative linear correlation with the variable "location" The variable with the closer correlation is the one with a coefficient closer to -1.

The variable "First income" with linear correlation coefficient r= -0.537 is the one with the strongest correlation to the variable "Location"

I hope this helps!

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)