2019 Nov P2 Q1

Question 1

The table below shows the monthly income (in rands) of

6

different people and the amount (in rands) that each person spends on the monthly repayment of a motor vehicle.

$\quad$ MONTHLY INCOME (IN RANDS)	$9\,000$	$13\,500$	$15\,000$	$16\,500$	$17\,000$	$20\,000$
$\quad$ MONTHLY REPAYMENT (IN RANDS)	$2\,000$	$3\,000$	$3\,500$	$5\,200$	$5\,500$	$6\,000$

1.1

Determine the equation of the least squares regression line for the data.

(3)

1.2

If a person earns

R14\,000

per month, predict the monthly repayment that the person could make towards a motor vehicle.

(2)

1.3

Determine the correlation coefficient between the monthly income and the monthly repayment of a motor vehicle.

(1)

1.4

A person who earns

R18\,000

per month has to decide whether to spend

R9\,000

as a monthly repayment of a motor vehicle, or not. If the above information is a true representation of the population data, which of the following would the person most likely decide on:

\quad A

Spend

R9\,000

per month because there is a very strong positive correlation between the amount earned and the monthly repayment.

\quad B

NOT to spend

R9\,000

per month because there is a very weak positive correlation between the amount earned and the monthly repayment.

\quad C

Spend

R9\,000

per month because the point

(18\,000\;;\,9\,000)

lies very near to the least squares regression line.

\quad D

NOT to spend

R9\,000

per month because the point

(18\,000\;;\,9\,000)

lies very far from the least squares regression line.

(2)

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