Question

Adjusted Gross Income ($1,000s)	Itemized Deductions ($1,000s)
22	9.6
27	9.6
32	10.1
48	11.1
65	15.5
85	19.7
120	25.5

a) Use the least squares method to develop the estimated regression equation that can be used to predict itemized deductions (in $1,000s) given the adjusted gross income (in $1,000s). (Round your numerical values to three decimal places.)

ŷ =

(b) Predict the reasonable level of total itemized deductions (in $1,000s) for a taxpayer with an adjusted gross income of $52,500. (Round your answer to two decimal places.)

$  thousand

Answer 1

X	Y	XY	X^2	Y^2
22	9.6	211.2	484	92.16
27	9.6	259.2	729	92.16
32	10.1	323.2	1024	102.01
48	11.1	532.8	2304	123.21
65	15.5	1007.5	4225	240.25
85	19.7	1674.5	7225	388.09
120	25.5	3060	14400	650.25

From the above table and formula we get thevalue are as:

n	7
sum(XY)	7068.40
sum(X)	399.00
sum(Y)	101.10
sum(X^2)	30391.00
sum(Y^2)	1688.13

b	0.1707
a	4.7116

ycap = a+ bx

ycap = 4.712 + 0.171x

b)

when x = 52.5

ycap = 4.712 + 0.171 * 52.5

ycap = 13.69