Question

A business analyst believes that December holiday sales in 2016 are a good predictor of December holiday sales in 2017. A random sample of 8 toys stores produced the following data where x is the amount of December holiday sales in 2016 and y is the amount of December sales in 2017, in dollars.

Show work method/steps, Computations, Calculations, Explain, list any applicable source/web applets, etc...

x	y
10257	11689
6556	6438
7224	8662
9987	9454
11568	12004
8453	8021
4235	6048
5576	4850

(a)   Find an equation of the least squares regression line. Round the slope and y-intercept value to two decimal places. Describe method for obtaining results.
(b)   Based on the equation from part (a), what is the predicted 2017 December holiday sales if the 2016 December holiday sales is 6,000 dollars? Show all work and justify your answer.
(c)   Based on the equation from part (a), what is the predicted 2017 December holiday sales if the 2016 December holiday sales is 20,000 dollars? Show all work and justify your answer.
(d)   Which predicted 2017 holiday sales that you calculated for (b) and (c) do you think is closer to the true predicted 2017 holiday sales and why?

Answer 1

#### By using R command

> x=c(10257,6556,7224,9987,11568,8453,4235,5576)
> x
[1] 10257 6556 7224 9987 11568 8453 4235 5576
> y=c(11689,6438,8662,9454,12004,8021,6048,4850)
> y
[1] 11689 6438 8662 9454 12004 8021 6048 4850
> fit=lm(y~x)
> fit

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x  
845.5971 0.9459

a) the least squares regression equation is:

y= 845.60+ 0.95*x

b)  the predicted 2017 December holiday sales when the 2016 December holiday sales is 6,000 dollars given by

y= 845.60+ 0.95*6000

y=845.60+5700

y=6545.6

the predicted 2017 December holiday sales is $6545.6

c) the predicted 2017 December holiday sales if the 2016 December holiday sales is 20,000 dollars is given by

y= 845.60+ 0.95*20000

y=845.60+19000

y=19845.60

the predicted 2017 December holiday sales is $19845.60

d) the predicted 2017 December holiday sales when the 2016 December holiday sales is 6,000 dollars is closer to the true predicted 2017 holiday sale.

Since This is the case of interpolation which is close to the true value while for the predicted sale when december sale $20000 is the case of extrapolation. The regression function may be different outside the range of the predictor variable.