Question

The worksheet "grocery" of "Assignment #4-2 (DATA)" gives the median store size (in square feet) by year for grocery stores. Note that this file is the same as the one given in Question 1.

Year	Size
1993	33.0
1994	35.1
1995	37.2
1996	38.6
1997	39.3
1998	40.5
1999	44.8
2000	44.6
2001	44.0
2002	44.0
2003	44.0
2004	45.6
2005	48.1
2006	48.8
2007	47.5
2008	46.8
2009	46.2
2010	46.0
2013	46.5

Step 1: Run the simple linear regression and find the slope of the sample regression equation. Give your answer to 4 decimal places.

Answer- .6783

Step 2- According to the sample regression line, a point estimate for the median grocery store size in 2012 is: (Give your answer to 1 decimal place.)

Answer- 49.9

Step 3- The standard error of fit is approximately?? (Give your answer to 3 decimal places.)

Answer 1

	X	Y	X * Y	X2	Ŷ	( Y - Ŷ )2
	1993	33.0000	65769	3972049	37	16.1071
	1994	35.1000	69989	3976036	38	6.7167
	1995	37.2000	74214	3980025	38	1.3688
	1996	38.6000	77046	3984016	39	0.2009
	1997	39.3000	78482	3988009	40	0.1820
	1998	40.5000	80919	3992004	40	0.0091
	1999	44.8000	89555	3996001	41.0832	13.8148
	2000	44.6000	89200	4000000	41.7615	8.0572
	2001	44	88044	4004001	42.4398	2.4343
	2002	44.0000	88088	4008004	43.11807	0.7778
	2003	44.0000	88132	4012009	43.79637	0.0415
	2004	45.6000	91382.4	4016016	44.47468	1.2664
	2005	48.1000	96440.5	4020025	45.15298	8.6849
	2006	48.8000	97892.8	4024036	45.83128	8.8133
	2007	47.5	95332.5	4028049	46.50958	0.9809
	2008	46.8	93974.4	4032064	47.18788	0.1505
	2009	46.2	92815.8	4036081	47.86618	2.7762
	2010	46	92460	4040100	48.54448	6.4744
	2013	46.5	93604.5	4052169	50.57939	16.6414
Total	38040	820.6	1643341.2	76160694	20419.69856	95.4982

Step 1

Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X² - (ΣX)² )
b = ( 19 * 1643341.2 - 38040 * 820.6 ) / ( 19 * 76160694 - ( 38040 )²)
b = 0.6783

a =( ΣY - ( b * ΣX ) ) / n
a =( 820.6 - ( 0.6783 * 38040 ) ) / 19
a = -1314.8413
Equation of regression line becomes Ŷ = -1314.8413 + 0.6783 X

Slope = b = 0.6783

Step 2

Ŷ = -1314.8413 + 0.6783 X

Ŷ = -1314.8413 + 0.6783 ( 2012 )
Ŷ = 49.9

Step 3

Standard Error of Estimate S = √ ( Σ (Y - Ŷ )² / n - 2) = √(95.4982 / 17) = 2.370