Regression Examples.docx

Regression

1.       A precast concrete kerb manufacturer monitors the number of identical kerbs produced per month by the company, together with the total cost of production. The following table shows the data collected for a random sample of 12 months.

(a)    Plot these data on a scatter diagram. Explain why this diagram would support the fitting of a regression equation of y on x.

(b)    Find an equation for the regression line of y on x in the form y = a + bx

( Use ∑x2 = 30786;   ∑xy = 41444 )

(c)    Given the selling price of each kerb produced is £2.20, find the level of output at which total income and total costs are equal. Interpret this value.

2.       Three trainee technicians independently carry out laboratory trials to examine the effect of temperature on the yield of an industrial process. The table shows the results obtained by each technician.

                            ∑x = 450       ∑y = 1254     ∑x2 = 20450    ∑xy = 49245

1. 1. (i) Draw a scatter diagram of the data. Label each point A, B, or C according to which technician carried out the trial.

(ii) Calculate the equation of the regression line of yield on temperature and draw the line on your scatter diagram.

(iii) Use your equation to estimate the yield for a temperature of 52oC.

2. 2. It is known that over this range of temperatures the relationship between yield and temperature is approximately linear. Comment on the performance of the three trainee technicians and on the reliability of the estimate made in a. (iii).
   3. An experienced and reliable technician carries out the trial at a temperature of 40oC and obtains a yield of 125 kg.  Plot this point on your scatter diagram, and without further calculation modify the estimate made in a.(iii). Comment on the reliability of your new estimate.