Question

The following table exhibits the age of antique furniture and the corresponding prices. Use the table to answer the following question(s). (Hint: Use scatter diagram and the Excel Trendline tool where necessary).

No. Years	Value($)
78	925
91	1010
83	970
159	1950
134	1610
210	2770
88	960
178	2010
124	1350
72	888

What is the expected value for a 90 year-old piece of furniture?

a. $934.56

b. $1029.36

c. $1002.45

d. $1033.21

Answer 1

Solution : Construct the equation using given information

x	y	xy	x^2	y^2
78	925	72150	6084	855625
91	1010	91910	8281	1020100
83	970	80510	6889	940900
159	1950	310050	25281	3802500
134	1610	215740	17956	2592100
210	2770	581700	44100	7672900
88	960	84480	7744	921600
178	2010	357780	31684	4040100
124	1350	167400	15376	1822500
72	888	63936	5184	788544
∑x	∑y	∑xy	∑x^2	∑y^2
1217	14443	2025656	168579	24456869

The values of x and y are

=∑x/n =1217/10 = 121.7

=∑y/n=14443/10 =1444.3

The values of SSxy, SSxx, SSyy are computed as follows:

SSxy=

=

=267942.90

SSxx=

=

=20470.10

SSyy=

=

=3596844.10

To find the regression line, we calculate a and b follows:

b= SSxy/SSxx

= 267942.90/20470.10

=13.08948

a= -b*

=1444.3-13.08948*121.7

=-148.69

Thus, our estimated line =a+bx is

= -148.69+13.08948*x

This is the regression equation

Expected value for value for x=90 year-old piece of furniture.

put x=90 in the regression equation

= 148.69+13.08948*90

=1029.36

$1029.36 is the expected value for a 90 year-old piece of furniture​​​​​​​

Correct option is b ) $1029.36​​​​​​​