Question:-

	You are interested in predicting processing time for an image 
	processing algorithm and have collected the following statistics 
        for a sample of images:
		processing time (ms): mean=350; std dev=40
		image complexity: mean=100; std dev=20
		correlation coefficient=0.6
	Making any necessary assumptions, determine the proportion of
	images of complexity 125 that required more than 410ms to be
	processed.

Solution:-

	You should first note that you are interested in predicting 
        processing time. Also, you interested in images of a particular
	complexity (i.e. 125). Hence processing time must be y and image 
        complexity must be x. 

	STEP 1: Determine the average processing time for images of 
		complexity 125. 

                There are two ways of doing this:

                1. Derive the regression equation and plug in 125:
                        b=0.6(40/20)=1.2
                        a=350-(1.2(100))=230
                   Hence:
                        y=230+1.2(125)=380
                   Processing time is therefore 380 for an image of
		   complexity 125. 

		2. You may also arrive at this answer by using the
                   following method:

                   Remember that slope = (rise/run). Since we know that
                   (xbar, ybar) is on the regression line we can compute
                   the rise since we know the run is 25:
                	rise/25=0.6(40/20)
			    rise=30
		   Hence benchmark score is 350+30=380.

	STEP 2: Determine the std dev of images of complexity 125. 

			SD(y|x)=sqrt(1-(0.6)**2)SD(y)
			SD(y|x)=sqrt(1-0.36)40
			       =32

	STEP 3: Assume NORMALITY and find the proportion that required more
		than 410ms processing time. 
			z=(410-380)/32=0.9375
		Hence (100-65.79)/2 or approximately 17% of images of
		complexity 125 required more than 410ms of processing time.