An IT company writes programs for apps. The time taken (in hours) to write the programs and the cost (in thousands of rands) are shown in the table below. TIME TAKEN (IN HOURS) 5 7 8 10 13 15 20 23 COST (IN THOUSANDS OF RANDS) 10 10 15 20 28 32 40 30 1.1 Determine the equation of the least squares regression line. 1.2 Use the equation of the least squares regression line to predict the cost, in rands, of an app that will take 16 hours to write. 1.3 Calculate the correlation coefficient of the data. 1.4 For each app that the company writes, there is a cost that is independent of the number of hours spent on writing the app. Calculate this cost (in rands).

NSC Mathematics Statistics: An IT company writes programs fo

An IT company writes programs for apps - NSC Mathematics - Question 1 - 2017 - Paper 2

Question 1

An IT company writes programs for apps. The time taken (in hours) to write the programs and the cost (in thousands of rands) are shown in the table below. TIME TAKE... show full transcript

Worked Solution & Example Answer:An IT company writes programs for apps - NSC Mathematics - Question 1 - 2017 - Paper 2

Step 1

Determine the equation of the least squares regression line.

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Answer

To find the equation of the least squares regression line, we first identify the coefficients from the data.

Let:

$a = 4.806$ (slope)
$b = 1.323$ (intercept)

The equation of the line in the form $y = ax + b$ is: $y = 4.81 + 1.32x$

Step 2

Use the equation of the least squares regression line to predict the cost, in rands, of an app that will take 16 hours to write.

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Answer

Using the regression equation:

$y = 4.81 + 1.32(16)$

Calculating: $y = 4.81 + 21.12 = 25.93$

Since the costs are in thousands of rands, we multiply by 1000: Cost = $25,930.

Step 3

Calculate the correlation coefficient of the data.

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Answer

The correlation coefficient (r) can be calculated using the formula:

$r = 0.949$

This indicates a strong positive correlation between time taken and cost.

Step 4

For each app that the company writes, there is a cost that is independent of the number of hours spent on writing the app. Calculate this cost (in rands).

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Answer

To find the fixed cost, we evaluate the cost at $x = 0$ , which is:

$y = 4.81$ Or in actual rands: Cost = $R 4,810$ .

An IT company writes programs for apps - NSC Mathematics - Question 1 - 2017 - Paper 2

Worked Solution & Example Answer:An IT company writes programs for apps - NSC Mathematics - Question 1 - 2017 - Paper 2

Determine the equation of the least squares regression line.

Use the equation of the least squares regression line to predict the cost, in rands, of an app that will take 16 hours to write.

Calculate the correlation coefficient of the data.

For each app that the company writes, there is a cost that is independent of the number of hours spent on writing the app. Calculate this cost (in rands).

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