The Swiss company Precision produces different types of watches. The monthly production costs and output from a production line for sports watches are as follows:

Required
1. (a) Draw a scatter diagram of costs against output.
(b) What does the diagram tell us?
2. (a) Calculate the formula of least-squares regression of costs on output and plot this line on the diagram.
(b) Explain your regression line.
3. Estimate the correlation coefficient, and R2, and explain their meanings.
4. The planned output of the factory for November is 600 sport watches.
(a) Forecast the costs for November.
(b) Explain the reliability of your forecast.

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Output X (units) Costs Y (£000) ΣΧ = 5,200 Jan 400 20 ΣΥ = 212 Feb 300 18 Mar May June 800 100 24 10 ΣΧ2 = 27,040,000 ΣY = 44,944 April 900 28 1000 32 July Aug Sept 300 700 200 20 28 12 EXY = = 128,800 Oct 500 20