Question

	Temperature (X)	Ice Cream Sales (Y)	X2	Y2	XY
	55	16	3025	256	880
	60	22	3600	484	1320
	65	25	4225	625	1625
	72	30	5184	900	2160
	75	37	5625	1369	2775
	83	45	6889	2025	3735
	85	59	7225	3481	5015
	92	76	8464	5776	6992
	95	89	9025	7921	8455
	100	95	10000	9025	9500
Total	782	494	63262	31862	42457

There is a well-known correlation between temperature and ice cream sales. The hotter it gets, the more ice cream people eat! A local ice cream shop hires you to predict how busy they will be on a future date given the forecast. Using temperature (X) and number of ice cream cones sold during the lunch hour (Y), fill in the blank spaces in following chart to assess this temperature / ice cream cone sales relationship:

What is the correct regression intercept (a)? (round to three decimal places here)

            A). 782.000

            B). 0.708

            C). -2.983

            D). 553.656

            E). -92.432

Answer 1

	X	Y	XY	X²	Y²
total sum	782	494	42457	63262	31862

sample size ,n    =10   

here,   x̅   =Σx/n =78.2000,ȳ = Σy/n =49.4

  

SSxx = Σx² - (Σx)²/n =2109.600

SSxy=Σxy - (Σx*Σy)/n =3826.200

SSyy = Σy²-(Σy)²/n =7458.400

estimated slope , ß1 = SSxy/SSxx =3826.2/2109.6=1.8137

  

intercept,ß0 = y̅-ß1* x̄ = 49.4 - 1.8137*78.2 = -92.432

so, answer is option E)