Question

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
75	20.8
85	24.7
95	30
105	34.6
115	39.5
125	44.1

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 155 grams of raspberries what is the expected Vitamin C content?   mgmg (round to the nearest tenth)

Answer 1

	Grams (X)	Vitamin C (Y)	X * Y	X2	Y2
	65	16.4	1066	4225	268.96
	75	20.8	1560	5625	432.64
	85	24.7	2099.5	7225	610.09
	95	30	2850	9025	900
	105	34.6	3633	11025	1197.16
	115	39.5	4542.5	13225	1560.25
	125	44.1	5512.5	15625	1944.81
Total	665	210.1	21263.5	65975	6913.91

Part a)

Equation of regression line is Ŷ = a + bX


b = 0.466
a =( Σ Y - ( b * Σ X) ) / n
a =( 210.1 - ( 0.4657 * 665 ) ) / 7
a = -14.229
Equation of regression line becomes Ŷ = -14.229 + 0.466 X

Part b)

When X = 155
Ŷ = -14.229 + 0.466 X
Ŷ = -14.229 + ( 0.466 * 155 )
Ŷ = 58.0