Question

Below is a table detailing the age of nine randomly selected houses and the insurance claims made on each home during the past five years.

Age of houses (years)	Insurance claims (1,000 of dollars)
72	10
35	6
45	8
39	5
22	3
100	21
57	8
74	15
37	9

1. Construct a scatterplot for this data set in the region to the right (with age of houses as the independent variable, and five-year insurance claim as the dependent variable.)
2. Based on the scatterplot, does it look like a linear regression model is appropriate for this data? Why or why not?      
3. Add the line of best fit (trend line/linear regression line) to your scatterplot. Give the equation of the trend line below. Then, give the slope value of the line and explain its meaning to this context.
4. Determine the value of the correlation coefficient. Explain what this value tells you about the two variables.
5. Based on the linear regression equation, what is the predicted amount of insurance claims during a five year period for a home of 60 years old? Show your calculation work.  
6. If there were $8,000 in insurance claims on a house during a five year period, what would be the expected age of that house?

Answer 1

A)

Based in the values given scatter plot is given as :

B)

As we can see that plot clearly shows that their is a linear relationship between "five-year insurance claim" and "age of houses". As if the one increases then the other also increases.

C)

let us denote X by five-year insurance claim

and Y by age of houses

Then we can fit the linear regression line by the following equation:

Regression equation of y on x is given by:

Where:

After calculating all these qunatities in calculator we get regression equation as

So the fitted line is :

Here value of slope is 0.2087

which implies that if we increase the age of house by one year then Insurance claims will increase by 0.2087 (in 1000 $)

Scatter plot with fitted regression line.

D)

Correlation coefficient between x and y is given by:

By calculating we get

As the value is greater than 0.90 . It suggests that their is a strong relationship between variable x and y

e)

From the fitted line we can find it for X = 60