Question

22

Statistics students in Oxnard College sampled 11 textbooks in the Condor bookstore, and recorded number of pages in each textbook and its cost. The bivariate data is shown below,

Number of Pages (xx)	Cost(yy)
513	65.43
323	34.53
751	87.61
619	70.09
671	80.81
914	101.54
310	44.1
321	51.31
243	45.73
496	63.56
528	59.08

A student calculates a linear model
yy =  xx + . (Please show your answers to two decimal places)

Use the model above to estimate the cost when number of pages is 575
Cost = $ (Please show your answer to 2 decimal places.)

21

The table below show data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a linear model that express Vitamin C content as a function of the weight of the Raspberries.

grams	Vitamin C content in mg
65	16.4
80	23
95	29.2
110	35.8
125	44.1
140	50.5
155	56.2

A) Find the regression equation: y=y= x+x+ Round your answers to 3 decimal places

B) Answer the following questions using your un-rounded regression equation.  

If we test 185 grams of raspberries what is the expected Vitamin C content?   mgmg (round to the nearest tenth)

20

A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).

The results of the regression were:

     y=ax+b
     a=-1.178
     b=21.882

Use this to predict the number of situps a person who watches 11 hours of TV can do (round to one decimal place)

Answer 1

22)

No. Of pages	Cost	(x-xbar)^2	(y-ybar)^2	(x-xbar)(y-ybar)
513	65.43	17.4724	2.1025	-6.061
323	34.53	37705.872	867.3025	5718.601
751	87.61	54671.792	558.3769	5525.1666
619	70.09	10367.312	37.3321	622.1202
671	80.81	23660.592	283.2489	2588.7906
914	101.54	157466.11	1410.7536	14904.5592
310	44.1	42923.552	395.2144	4118.7384
321	51.31	38486.592	160.5289	2485.6006
243	45.73	75174.672	333.0625	5003.785
496	63.56	448.5924	0.1764	8.8956
528	59.08	117.0724	24.01	-53.018
5689	703.79	441039.64	4072.1087	40917.1782
517.18	63.98

The regression equation is given by,

b = 40917.1782 / 441039.64

= 0.09

= 63.98 - 0.09* 517.18

= 17.43

yy = 17.43 + 0.09 xx (ans)

The cost when number of pages(xx) is 575
Cost = 17.43 + 0.09*575 = 69.18 (ans)

21)

grams (x)	Vitamin C (y)	(x-xbar)^2	(y-ybar)^2	(x-xbar)(y-ybar)
65	16.4	2025	402.4036	902.7
80	23	900	181.1716	403.8
95	29.2	225	52.7076	108.9
110	35.8	0	0.4356	0
125	44.1	225	58.3696	114.6
140	50.5	900	197.1216	421.2
155	56.2	2025	389.6676	888.3
770	255.2	6300	1281.8772	2839.5
110	36.46

a) The regression equation is given by,

  

b = 2839.5 / 6300 = 0.451

  

a = 36.46 - 0.451*110 = -13.153

The regression equation is,

y = -13.153 + 0.451 x

b) x = 185 grams

y = -13.153 + 0.4507 * 185 = 70.226

20) A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).

The results of the regression were:

  y=ax+b a=-1.178   b=21.882 

The regression equation is given by,

y = -1.178 + 21.882 x

The number of situps a person who watches 11 hours of TV can do is

y = -1.178 + 21.882*11 = 239.5 (ans)

****If you have any queries or doubts please comment below, if you're satisfied please give a like. Thank you!