SOLUTION: Linear Regression The table below shows the value, V , of an investment (in dollars) n years after 1990. n 1 3 7 12 14 19 V 21120 20148.8 19440 18581.2 17480

Question 1197140: Linear Regression
The table below shows the value,
V
, of an investment (in dollars)
n
years after 1990.
n
1 3 7 12 14 19
V
21120 20148.8 19440 18581.2 17480 15276
Determine the linear regression equation that models the set of data above, and use this equation to answer the questions below. Round to the nearest hundredth as needed.
Based on this regression model, the value of this investment was $
in the year 1990.

Based on the regression model, the value of this investment is
Select an answer
at a rate of $
per year.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

I'll use x and y in place of n and V
x = n
y = V

x = number of years after 1990
y = value of an investment (in dollars)

Given Data:

x	y
1	21120
3	20148.8
7	19440
12	18581.2
14	17480
19	15276

There are n = 6 rows of data to represent the sample size.

We'll form the following columns:
x^2
xy
The x^2 column is where we square each x value
eg: 19 squares to 19^2 = 19*19 = 361
The xy column has us multiply each x and y value together (separately per row).
Eg: 3*20148.8 = 60446.4 in the second row of this column.

x	y	x^2	xy
1	21120	1	21120
3	20148.8	9	60446.4
7	19440	49	136080
12	18581.2	144	222974.4
14	17480	196	244720
19	15276	361	290244

Use of a spreadsheet program is strongly recommended.

Then compute the following sums
P = sum of the x values = 56
Q = sum of the y values = 112046
R = sum of the x^2 values = 760
S = sum of the xy values = 975584.8

The regression line is of the form y = mx+b
m = slope =

b = y intercept =

Let's find the slope

approximately

Now compute the y intercept

approximately

The regression line is y = -295.69x + 21434.14 approximately
As a quick shortcut, you can use technology (eg: calculator or spreadsheet) to calculate the equation for the regression line.

x = 0 corresponds to the year 1990
Plug it in to find that y = 21434.14 which is exactly the y intercept.

Based on the regression model, the estimated value of the investment was about $21434.14 in the year 1990.

The slope tells us how much the investment goes up or goes down.
In this case, a negative slope means the investment is decreasing in value. As x goes up y goes down.
The slope is roughly m = -295.69 to represent a decrease of $295.69 per year.

----------------------------------------------------------------------------

Answers:
$21434.14 was the approximate value of the investment in the year 1990 (estimate according to the regression line)

The investment decreases at a rate of about $295.69 per year (estimate according to the regression line)

RELATED QUESTIONS
The table below shows the value,V, of an investment (in dollars) n years after 1994. (answered by Theo)

Exponential Regression The table below shows the value, V, of an investment (in dollars) (answered by jim_thompson5910)

Math Encrypt the message “BYE” using the encryption e equals left parenthesis 5 m... (answered by math_tutor2020)

MAT 145: Topics In Contemporary Math QUESTION 12 Convert the message (answered by ikleyn)

MAT 145: Topics In Contemporary Math QUESTION 12 Convert the message... (answered by greenestamps)

The value,$V, of a house n years after it was built is given by the formula V =... (answered by MathLover1,ikleyn)

Bill places $10,000 in an investment account earning an annual rate of 5.1% compounded... (answered by texttutoring)

A new 24000 dollars car depreciates in value 5000 dollars per year. Construct a linear... (answered by oscargut)

Solve the problem. A rare baseball card was sold in 1990 for $285,000. The card was... (answered by nerdybill)