1. Given the correlation coefficient 0.9940.994 and the linear regression equation =2121.81x=2121.81, compute the coefficient of determination.

r2=2=

Round to 4 decimal places.

2. Given the correlation coefficient 0.7940.794 and the linear regression equation =16.4+1.58x=16.4+1.58, compute the coefficient of determination.

r2=2=

Round to 4 decimal places.

3. 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:

=121.090.57246xR2=0.894=121.090.572462=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

(click to select)increasesdecreases

. The correlation between the two variables is

(click to select)positivenegative

. b. Calculate the correlation coefficient and determine if the relationship between the two variables is strong, moderate or weak. r==

, the relationship is

(click to select)strongmoderateweak

.

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 $88,900?

Round to the nearest dollar.

4. The owners of an e-business have been successful in selling fashion products but are now venturing into another domain. Knowing that the impact of advertising on profit cannot be overemphasized, they are interested in determining the right amount to allocate to advertising for the new business. Based on a monthly report from the fashion e-business, a regression analysis of monthly profit (in thousands of dollars) on advertising spending (in hundreds of dollars) produced the following results:

slope	y-intercept	r
1.36	2.578	0.7377

where y = profit (in $1000s) x = advertising spending (in $100s)

a. State the least-squares regression line for the data. ==

++

x

b. Interpret the value of the slope as it relates to this problem.

For every $1 increase in advertising spending, there is a $1.36 increase in profit.

For every $100 increase in advertising spending, there is a $1,360 increase in profit.

For every $100 increase in advertising spending, there is a $136 increase in profit.

For every $1,000 increase in advertising spending, there is a $136 increase in profit.

c. Compute and interpret the coefficient of determination. R2=2=

Round to 4 decimal places

d. Predict the monthly profit for a month when advertising is $2,300.

Round to the nearest cent

e. If the expected profit in a particular month is $51,538, about how much should be set aside for advertising that month?

Round to the nearest cent