Q6 The following table gives data from the 2011 UK Census on

Q6

The following table gives data from the 2011 UK Census, on a simple random sample of 12 parliamentary constituencies drawn from all the constituencies in England and Wales. The data for each constituency are x, the percentage of households in the constituency where all the residents are of age 65 and over, and y, the percentage of the dwellings in the constituency that are detached houses.

For these data ?x? = 6227.64, ?y? = 9751.56 and ?xy = 7419.36.

Choose the option that is closest to the slope of the least squares regression line for these data, rounded to 3 significant figures, treating x as the explanatory variable and y as the response variable.

Select one:

A) 0.325

B) 1960

C) 322

D) 636

E) 1.97

F) -18.3

G) 0.507

Solution

Slope(b) = (N?XY - (?X)(?Y)) / (N?X² - (?X)²)

             = (12 x 7419.36 - 266.2 x 305.8) / (12 x 6227.64 - (266.2)²) = 1.97