A researcher uses a regression equation to predict electric bill costs (in dollars) based on the age of the home (in years). The correlation between predicted electric bills and age of the home is 0.60. How should this finding be interpreted?

36% of the variability in electric bills can be explained by the age of home

Explanation:

Given:

The coefficient of determination measures the proportion of variation in the dependent variable that is predictable from the independent variable.

The coefficient of determination is equal to ;

In this situation we have the correlation = 0.6 , hence our coefficient is or 0.36. Therefore, 36% of the variability in electric bills can be explained by the age of home

Correct Question:  

A company produces two products. Product A sells for $25, has variable costs of $15, requires 2 machine hours to produce and the market is limites to 8,000 units. Product B sells for $35, has variable costs of $20, requires 5 machine hours to produce, and the market is limited to 6,000 units. 40,000 machine hours are available. What should the company produce of Product A and B?

8000 units of product A and 4,800 units of product B should be produced.

Explanation:

Product A sells for $25 but cost $15 to produce. It means there is a contribution margin of $10 per unit (i.e $25-$15)

since it takes 2hours to produce product A we have 10/2= 5 products per machine hour.

$10 × 8000 units = $80,000 (in profits)

on the other hand, if product B is to be sold at $35 per unit but has a production cost of $20, it means a contribution margin of $15(i.e $35-$20) is embedded in each $35 sale. If the company produces 4,800 units of this product B, it means that the company has

$15 × 4,800 units = $72, 000

Since the aim of the company's production is to make profit, it is very clear that product A should be produced compared to product B because it has a higher contribution margin