Question

Consider the following regression equation representing the linear relationship between the Canada Child Benefit provided for a married couple with 3 children under the age of 6, based on their annual family net income: ŷ =121.09−0.57246xR2=0.894 where y = annual Canada Child Benefit paid (in $100s) x = net annual family income (in $1000s) Source: Canada Revenue Agency

a. As the net annual family income increases, does the Canada Child Benefit paid increase or decrease? Based on this, is the correlation between the two variables positive or negative? The Canada Child Benefit paid . The correlation between the two variables is .

b. Calculate the correlation coefficient and determine if the relationship between the two variables is strong, moderate or weak. r= 0 , the relationship is . Round to 3 decimal places c. Interpret the value of the slope as it relates to this relationship. For every $1 increase in annual family net income, there is a $0.57246 decrease in the Canada Child Benefit paid. For every $100 increase in annual family net income, there is a $572.46 decrease in the Canada Child Benefit paid. For every $1000 increase in annual family net income, there is a $57.746 decrease in the Canada Child Benefit paid. For every $100 increase in annual family net income, there is a $57,246 decrease in the Canada Child Benefit paid. d. What will be the estimated Canada Child Benefit be (in dollars) for a married couple with 3 children under the age of 6 if the net annual family income is $86,100? $0

Answer 1

Given equation

y=121.09 - 0.57246*family net income

R2 = 0.894

Answer(a):

From the given equation, we have β1= - 0.57246, we can see that the regression coefficient for family net income is negative which indicates that there is negative relationship between Canada child benefit and family net income.

We can interpret that as the net annual family income increases, the Canada Child Benefit paid decreases and we the know the property that regression and correlation coefficients, both have same direction (i.e. similar signs), hence the correlation coefficient between the two variables will also be negative.

Answer(b): we have R2=0.894 which is square of correlation coefficient. The correlation coefficient will be the square root of R2.

In previous answer we have established that correlation will be negative, hence the final correlation coefficient is -0.946.

We can see that correlation coefficient is very high in negative direction i.e. close to -1, so we can conclude that the relationship between the two variables is strong and negative.

Answer(c): Interpretation the value of the slope as it relates to this relationship

The correct answer is

For every $1000 increase in annual family net income, there is a $57.746 decrease in the Canada Child Benefit paid.

Answer(d): we have net annual family income=$86100 i.e. 86.1 (in $1000s)

So the estimated Canada child benefit (in $100s) will be

y=121.09-0.57246*86.100

y=121.09-49.2881

y=71.8012

So, the estimated Canada Child Benefit (in dollars) is $7180.12 for a married couple with 3 children under the age of 6 if the net annual family income is $86,100.