The owner of a small company wishes to establish whether advertising in a regional newspaper is effective. The table below shows the amount spent on advertising and the corresponding sales figures for the last 9 years. Amount spent on advertising (in rands) (x) Sales (in rands) (y) 21 300 23 700 24 800 30 540 24 100 48 600 22 000 35 250 29 000 311 500 326 700 349 200 470 000 316 100 564 200 487 300 392 000 1.1.1 Determine the equation of the least squares regression line for the data. 1.1.2 Predict the sales for a year in which the company will spend R28 500 on advertising. 1.1.3 Write down the correlation coefficient of the data. 1.1.4 Describe the association between the amount spent on advertising in the regional newspaper and the sales of this company.

NSC Mathematics Statistics: The owner of a small company wis

The owner of a small company wishes to establish whether advertising in a regional newspaper is effective - NSC Mathematics - Question 1 - 2023 - Paper 2

Question 1

The owner of a small company wishes to establish whether advertising in a regional newspaper is effective. The table below shows the amount spent on advertising and ... show full transcript

Worked Solution & Example Answer:The owner of a small company wishes to establish whether advertising in a regional newspaper is effective - NSC Mathematics - Question 1 - 2023 - Paper 2

Step 1

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

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Answer

To determine the least squares regression line, we need to fit a linear equation of the form $y = a + bx$ , where $y$ represents sales and $x$ represents advertising spending.

Using the formulas for a and b:

1.1 Calculate the slope (b): $b = rac{n( ext{Sum of } xy) - ( ext{Sum of } x)( ext{Sum of } y)}{n( ext{Sum of } x^2) - ( ext{Sum of } x)^2}$

2.1.1 Calculate the y-intercept (a): $a = ar{y} - b ar{x}$

The resulting linear equation is $y = 1730.22 + 13.96x$ .

Step 2

Predict the sales for a year in which the company will spend R28 500 on advertising.

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Answer

Using the regression equation generated: $y = 1730.22 + 13.96(28500)$

Calculate: $y = 1730.22 + 396.78 imes 28500 = 399 599.64$ The predicted sales for R28 500 spent on advertising is approximately R399 599.64.

Step 3

Write down the correlation coefficient of the data.

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Answer

The correlation coefficient (r) for the data is calculated to be $r = 0.9800$ .

Step 4

Describe the association between the amount spent on advertising in the regional newspaper and the sales of this company.

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Answer

There is a very strong positive correlation between the amount spent on advertising and sales. As advertising spending increases, sales tend to increase significantly.

The owner of a small company wishes to establish whether advertising in a regional newspaper is effective - NSC Mathematics - Question 1 - 2023 - Paper 2

Worked Solution & Example Answer:The owner of a small company wishes to establish whether advertising in a regional newspaper is effective - NSC Mathematics - Question 1 - 2023 - Paper 2

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

Predict the sales for a year in which the company will spend R28 500 on advertising.

Write down the correlation coefficient of the data.

Describe the association between the amount spent on advertising in the regional newspaper and the sales of this company.

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