Question

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significa correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the number of stories of six notable buildings in a city. Height, x 758 621 518 510 492 483 (a) x = 499 feet (b) x = 644 feet Stories, y 51 47 46 37 35 (c) x = 321 feet (d) x = 726 feet 43 Find the regression equation. ye X + (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.)

Answer 1

1.

	x	y		x2	y2	xy
	758	51		574564	2601	38658
	621	47		385641	2209	29187
	518	46		268324	2116	23828
	510	43		260100	1849	21930
	492	37		242064	1369	18204
	483	35		233289	1225	16905
sum	3382	259		1963982	11369	148712
average	563.6667	43.16667		327330.3	1894.833	24785.33

The regression equation is given by Y = a +bX where,

Y is the estimated y

b= slope of the regression equation

b=[average of xy -(average of x)*(average of y)]/[average of x^2-((average of x)^2]

=[24785.33-563.6667*43.16667]/[327330.3-563.6667^2]

=0.0472

Intercept =a

= (average of y) -b*(average of x)

=43.16667-.047212*563.6667

= 16.55

Thus, the regression equation is Y = 16.55 + 0.0472X

SCATTER PLOT ; oN X Axis is the height in feet and on y axis is the no. of stories

60 50 40 300 20 10 0 0 100 200 300 400 500 600 700 800

a. When x = 499, Y = 16.55 + 0.0472*499 =40.10 =40 stories

b. When x = 644, Y = 16.55 + 0.0472*644 =46.946 =47 stories

c. When x = 321, Y = 16.55 + 0.0472*321 =31.7 = 32 stories

d. When x = 726, Y = 16.55 + 0.0472*726=50.81 =51 stories

Only one question at a time, please give the remaining as another questions

thank you.