Question

Consider the following data. Monthly natural gas cost, TL 246 230 269 284 298 322 355 242 Area of apartment, m2 90 85. 105 110 120 130 140 95 a) Draw the scatter diagram and decide the type of regression function. b) Obtain the least quares regression function. c) Forecast the monthly natural gas cost of an 125 m2 apartment. d) Calculate the determination and correlation coefficients and interpret them.

Answer 1

Ans:

a)

cost(y) y 2.1815x+42.146 R 0.9822" 350 300 250 50 20 40 80 TiHi 120 140160

Froma above data,it best fit the linear regression function.

b)

	Area(x)	cost(y)	xy	x^2	y^2
1	90	246	22140	8100	60516
2	85	230	19550	7225	52900
3	105	269	28245	11025	72361
4	110	284	31240	12100	80656
5	120	298	35760	14400	88804
6	130	322	41860	16900	103684
7	140	355	49700	19600	126025
8	95	242	22990	9025	58564
Total=	875	2246	251485	98375	643510

slope,b=(8*251485-875*2246)/(8*98375-875^2)=2.1815

y-intercept,a=(2246-2.18152*875)/8=42.146

Regression eqn:

y'=2.1815x+42.146

c)when x=125 m^2

y'=2.1815*125+42.146=314.83

d)

correlation cofficient,r=(8*251485-875*2246)/SQRT((8*98375-875^2)*(8*643510-2246^2))=0.9911

cofficient of determination,r^2=0.9911^2=0.9822 or 98.22%,which indicates that 98.22% of the linear variation in monthly cost is explained by the area.