Maths Support: Linear regression

Question 1

To monitor its staff appraisal methods, a personnel department compares the results of the tests carried out on employees at their first appraisal with an assessment score of the same individuals two years later. The resulting data are as follows:

Employee	$\var{obj[0]}$	$\var{obj[1]}$	$\var{obj[2]}$	$\var{obj[3]}$	$\var{obj[4]}$	$\var{obj[5]}$	$\var{obj[6]}$	$\var{obj[7]}$
First Test $(X)$	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$	$\var{r1[6]}$	$\var{r1[7]}$
Later Score $(Y)$	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$	$\var{r2[5]}$	$\var{r2[6]}$	$\var{r2[7]}$

a)

Calculate the equation of the best fitting regression line:

\[Y = a + b \times X.\] Find $a$ and $b$ to 5 decimal places, then input them below to 3 decimal places. You will use these approximate values in the rest of the question.

$b=\;$question.score feedback.none Expected answer: , $a=\;$question.score feedback.none Expected answer: (both to 3 decimal places.)

You are given the following information:

First Test$(X)$	$\sum x=\;\var{t[0]}$	$\sum x^2=\;\var{ssq[0]}$
Later Score$(Y)$	$\sum y=\;\var{t[1]}$	$\sum y^2=\;\var{ssq[1]}$

Also you are given $\sum xy = \var{sxy}$.

Click on Show steps if you want more information on calculating $a$ and $b$. You will not lose any marks by doing so.

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b)

What is the predicted Later score for employee $\var{obj[ch]}$ in the First test?

Use the values of $a$ and $b$ you input above.

Enter the predicted Later score here: (to 2 decimal places)

Expected answer:

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c)

Use the result above to calculate the residual value for employee $\var{obj[ch]}$.

Click on Show steps to see what is meant by the residual value if you have forgotten. You will not lose any marks by doing so.

Residual value = (to 2 decimal places).question.score feedback.none Expected answer:

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Score: 0/1

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Question 2

Employee	$\var{obj[0]}$	$\var{obj[1]}$	$\var{obj[2]}$	$\var{obj[3]}$	$\var{obj[4]}$	$\var{obj[5]}$	$\var{obj[6]}$	$\var{obj[7]}$	$\var{obj[8]}$	$\var{obj[9]}$
First Test $(X)$	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$	$\var{r1[6]}$	$\var{r1[7]}$	$\var{r1[8]}$	$\var{r1[9]}$
Later Score $(Y)$	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$	$\var{r2[5]}$	$\var{r2[6]}$	$\var{r2[7]}$	$\var{r2[8]}$	$\var{r2[9]}$

a)

Calculate the equation of the best fitting regression line:

\[Y = a + b \times X.\] Find $a$ and $b$ to 5 decimal places, then input them below to 3 decimal places. You will use these approximate values in the rest of the question.

$b=\;$question.score feedback.none Expected answer: , $a=\;$question.score feedback.none Expected answer: (enter both to 3 decimal places).

You are given the following information:

First Test$(X)$	$\sum x=\;\var{t[0]}$	$\sum x^2=\;\var{ssq[0]}$
Later Score$(Y)$	$\sum y=\;\var{t[1]}$	$\sum y^2=\;\var{ssq[1]}$

Also you are given $\sum xy = \var{sxy}$.

Click on Show steps if you want more information on calculating $a$ and $b$. You will not lose any marks by doing so.

(Your score will not be affected.)

This feedback is based on your last submitted answer. Submit your changed answer to get updated feedback.

Score: 0/2

Unanswered

Or, you could:

There's nothing more to do from here.

b)

What is the predicted Later score for employee $\var{obj[ch]}$?

Use the values of $a$ and $b$ you input above.

Enter the predicted Later score here: (to 2 decimal places)

Expected answer:

This feedback is based on your last submitted answer. Submit your changed answer to get updated feedback.

Score: 0/1

Unanswered

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There's nothing more to do from here.

c)

Use the result above to calculate the residual value for employee $\var{obj[ch]}$.

Click on Show steps to see what is meant by the residual value if you have forgotten. You will not lose any marks by doing so.

Residual value = (to 2 decimal places).question.score feedback.none Expected answer:

(Your score will not be affected.)

This feedback is based on your last submitted answer. Submit your changed answer to get updated feedback.

Score: 0/1

Unanswered

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Advice

Total	0/4

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Maths Support: Linear regression

Question 1

Question 1

a)

b)

c)

Advice

Question 2

Question 2

a)

b)

c)

Advice