# CORRELATION AND REGRESSION 2

FORTS 7 QUESTIONS – CORRELATION AND REGRESSION

1. The management of Huddwink Hessian Ltd believes that the cost of servicing and delivering an order varies in direct proportion to the size of the order.

The following data which has been randomly sampled from recent orders is considered typical:

 Size of order (units) Order handling cost £ 36 929 85 2215 69 1679 57 1224 95 1988 76 2002 72 1857 74 1580

You are required to:

(a)   Find the sample correlation coefficient (r).

(b)   Test, at the 5% level of significance, the null hypothesis that there is no linear relationship between order handling cost and size of order.

(c)   Calculate the “Goodness of Fit” for the data.

(d)   Calculate the equation of the least squares regression line:
Order handling cost = A + (B × Size of order).

(e)   Estimate from your equation the order handling cost for an order of 79 units.

1. For the period 19X0 to 19X9, the coal production, number of coalminers killed underground and average weekly earnings of underground workers were as follows:
 Year Coal production (million tons) Persons killed underground Average weekly earnings (£) 19X0 123 87 234 19X1 120 70 266 19X2 100 75 306 19X3 114 79 381 19X4 100 70 407 19X5 110 63 470 19X6 110 60 528 19X7 159 113 584 19X8 96 55 642 19X9 99 45 959

(i)    With respect to the relationship between coal production and number of persons killed:

(a)  Find the sample correlation coefficient (r).

(b)  Test, at the 10% level of significance, whether there is a linear relationship between coal production and number of persons killed.

(c)   Calculate the “Goodness of Fit” for the data.

(d)  Calculate the equation of the least squares regression line:
Persons killed = A + (B × Coal production (million tons)).

(ii)   With respect to the relationship between coal production and average weekly earnings:

(a)  Find the sample correlation coefficient (r).

(b)  Test, at the 1% level of significance, whether there is a linear relationship between coal production and average weekly earnings.

(c)   Calculate the “Goodness of Fit” for the data.

(d)  Calculate the equation of the least squares regression line:
Average weekly earnings = A + (B × Coal production (million tons)).

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