Question

Devin invested money into a bank account. The table below is the value of Devin’s investment over time.

Answer 1

given

Table which shows the value of Devin's investment over time.

Find

a) type of equation

b) regression equation

c) y - intercept

d) strong correlation or not?

e) value of investment after 6 years?

Explanation

let X = year

Y = value

$\begin{gathered} \sum_^X=72 \\ \\ \sum_^Y=242300 \\ \\ \sum_^X\cdot Y=3568900 \\ \sum_^X^2=1038 \\ \sum_^Y^2=12600850000 \end{gathered}$

a) linear equation would best fit the data.

b) equation of regression line is y = ax + b

where

$\begin{gathered} b=\frac{(n\sum_^XY-\sum_^X\sum_^Y)}{(n\sum_^X^2-(\sum_X)^2)} \\ \\ b=3800.575 \end{gathered}$

and

$\begin{gathered} a=\frac{(\sum_^Y-(b\sum_^X))}{n} \\ \\ a=-5223.563 \end{gathered}$

so , equation of regression is

y = -5223.563 + 3800.575X

c) y- intercept is the value when x = 0

so , y - intercept is -5223.563

d) there is strong and positive correlation between variables.

because

$r=\frac{(N\sum_^XY)-\sum_^X\sum_^Y}{\sqrt{N\sum_(X)^2-(\sum^X)^2-N\sum_(Y)^2-(\sum^Y)^2}}$

r = 0.945

e) when X = 6

$\begin{gathered} Y=-5223.563+3800.575\times6 \\ Y=17579.89\approx17580 \\ \end{gathered}$

Final Answer

Hence , the above are the required answers