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 - NSC Mathematics - Question 1 - 2019 - Paper 2
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 vehic... show full transcript
Worked Solution & Example Answer: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 - NSC Mathematics - Question 1 - 2019 - Paper 2
Step 1
Determine the equation of the least squares regression line for the data.
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Answer
To find the least squares regression line, we can use the formula:
y=a+bx
where:
y is the dependent variable (monthly repayment),
x is the independent variable (monthly income),
a is the y-intercept and can be found using the formula:
a = ar{y} - bar{x}
b is the slope and can be calculated using:
b=n(∑x2)−(∑x)2n(∑xy)−(∑x)(∑y)
After performing the calculations, we find:
b=0.41a=−1946.88
Thus, the regression equation is:
y=−1946.88+0.41x
Step 2
If a person earns R14 000 per month, predict the monthly repayment that the person could make towards a motor vehicle.
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Answer
Using the regression equation:
y=−1946.88+0.41(14000)
Calculating the repayment:
y=−1946.88+5740=R3727.16
Thus, the predicted monthly repayment is approximately R3 727.16.
Step 3
Determine the correlation coefficient between the monthly income and the monthly repayment of a motor vehicle.
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Answer
The correlation coefficient r can be computed using:
r=[n(∑x2)−(∑x)2][n(∑y2)−(∑y)2]n(∑xy)−(∑x)(∑y)
After calculating, we find:
r=0.946
This indicates a strong positive correlation between monthly income and repayment.
Step 4
A person who earns R18 000 per month has to decide whether to spend R9 000.
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Answer
Based on the interpretation of the correlation and position relative to the regression line,
Option D is the most logical choice.
NOT to spend R9 000 per month because the point (18 000 ; 9 000) lies very far from the least squares regression line.
