Question

At a used dealership, let X be an independent variable representing the age in years of a motorcycle and Y be the dependent variable representing the selling price of used motorcycle. The data is now given to you. X = {5, 10; 12, 14, 15} Y = {500, 400, 300, 200, 100} A) Estimate the parameters of the model B) Write the prediction equation C) Calculate SSE.

Answer 1

Answer:

a)

Alpha (α) = 728.02

Beta (β) = -38.22

b) The prediction equation is:

Y = 728.02 - 38.22 X

c)

SSE = 8280.25

Step-by-step explanation:

Since X is the independent variable (which is representing the age in years of a motorcycle), and Y is the dependent variable (which is representing the selling price of used motorcycle).

Then, we can infer that, the model is a linear regression model. Hence we fit the equation below:

                                            Y = α + β X + ε

Where:

α & β are the parameters of the model. Mathematically,

α = $\bar{Y} - \beta \bar{X}$

$\beta = \frac{n \sum{XY} - \sum{X}\sum{Y}}{n\sum{X^2} - (\sum{X})^2}$,

By:

$\bar{Y} = \frac{\sum{Y}}{n} \; and\; \bar{X} = \frac{\sum{X}}{n}$

As given, we can obtain all the information from the data given. However, to make it fast, please see the R codes for the solution below:

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#.......................................              R codes              .................................................#

X = c(5, 10, 12, 14, 15)

Y = c(500, 400, 300, 200, 100)

mod = lm(Y~X)

summary(mod)# ... this produce all the model results

aov(mod)#.. this produce the SSE

anova(mod)#.. this produce the SSE

########################################################