# Linear Regression Model

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Problem:

We are using a linear regression model (time series) to predict sales of our "WW" brand. Historically, sales of this product for the period 1982 to date (1982 through summer 2003; assume 1982 was year one) have been approximated by the following data (in thousands of units):

Y = 3.984X + 2.994

Sy = .677

r2 (R squared) = .24

(A) What would be your basic forecast of sales for 2005 (year 23)?

(B) If you wished to add the condition of 95% confidence in your 2005 forecast, what would be the range of prediction?

(C) Would you expect r2 (r squared) to have been computed using Pearson's or Spearman's mthod? Why?

(D) Suggest an alternative to time series that might improve the predictivity of the model. An r2 (r squared) of .24 isn't exactly stellar.

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##### Solution Summary

The solution answers different questions regarding the given data on sales. It discusses what the basic forecast would be for that year, the range of prediction etc.

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Problem:

We are using a linear regression model (time series) to predict sales of our "WW" brand. Historically, sales of this product for the period 1982 to date (1982 through summer 2003; assume 1982 was year one) have been approximated by the following data (in thousdands of units):

Y = 3.984X + 2.994 (1)

Sy = .677

r2 (R squared) = .24

(A) What would be your basic forecast of sales ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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