A study was commissioned to investigate the characteristics of properties that are for sale. Data was collected on 60 houses and the following variables recorded.

Column 1 Value Value of house in thousands of dollars
Column 2 Lot size Size of the property
Column 3 Bed Number of bedrooms in house
Column 4 Bath Number of bathrooms in house
Column 5 Rooms Total number of rooms in the house
Column 6 Age Age of house in years
Column 7 Fireplace Number of fireplaces

Question 1:

For the variable Value find the:

a) mean,
b) median,
c) range,
d) standard deviation and
e) variance.

Question 2:

Estimate with 95% confidence the average age of a house.

Question 3:

Using an appropriate hypothesis test, at a 5% level of significance, can you conclude that there is any difference between the average value between houses that have a fireplace (Fireplace = 1) and houses that don't have a fireplace (Fireplace = 0)?

Question 4:

(a) Estimate the regression equation to predict the Value (y) from the number of Rooms (x).

(b) Determine the coefficient of determination and interpret its value.

(c) Does the data provide evidence that the slope of the equation from part a) is positive? Perform an appropriate hypothesis test using a 5% level of significance.