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# Best Model

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We are predicting the number of units sold for a local factory that produces snowmobiles. The available annual data are the expenses (in \$000), the number of employees, and the rainfall (in in.). Find the best model using the following table.

Year Expenses #Employees Rainfall Units Sold
1987 5300 230 34 5836
1988 4700 227 39 5921
1989 6500 229 32 5745
1990 6800 233 41 5990
1991 6450 236 36 6312
1992 7250 238 38 6151
1993 7600 240 35 6423
1994 7800 215 38 5975
1995 8100 216 33 6045
1996 7900 218 37 6123
1997 7850 217 34 6215
1998 8450 214 35 6187
1999 7900 216 36 6279
2000 8600 217 39 6386
2001 8850 216 40 6479
2002 8900 218 42 6332
2003 9150 217 36 6408

a. "Year" may be used as an x-variable.

b. The overall model is significant.

c. All x-variables are significant.

d. The coefficient of determination is greater than .7.

e. If we eliminate a variable, rainfall would be our first choice.

https://brainmass.com/statistics/analysis-of-variance/find-best-model-79312

#### Solution Preview

I use the econometric method to build a sales model given the data provided. I explore the individual variables, their relationships to one another, then provide results from a few different specifications. Theory asside it seems that time and number of employees are the best predictors of how many snowmobiles this firm will sell.

I usually start a project like this by looking at the data in a matrix. First, look at the last row (see the blue arrow). This row gives us an idea about the relationship between our dependent variable "Sales" and our independent variables. First we see a strong relationship between sales and date. Nice and linear. As time goes by sales steadily increase although there is a dip in 1993. Some sort of shock. I would want to include this trend variable in the model. Next, sales and expenses seem to be positively correlated too. Sales and number of employees is not as obvious, we'll explore this more in a second. There does appear to be a positive relationship between sales and rainfall. But it is tenuous.

When constructing a model we have two concerns the data and the theory. Regarding theory we have to ask "what causes snowmobile sales?" I would think a time trend variable would be good to include. The expenses that the company faces is certainly correlated to sales because as you sell more your costs are higher. However I don't know if I would say higher expenses for a firm leads to higher sales. It is more likely that high sales lead to higher expenses. If those are in fact firm expenses then I don't know that I would include it unless you can ...

#### Solution Summary

We are predicting the number of units sold for a local factory that produces snowmobiles. The available annual data are the expenses (in \$000), the number of employees, and the rainfall (in in.). Find the best model using the following table.

Year Expenses #Employees Rainfall Units Sold
1987 5300 230 34 5836
1988 4700 227 39 5921
1989 6500 229 32 5745
1990 6800 233 41 5990
1991 6450 236 36 6312
1992 7250 238 38 6151
1993 7600 240 35 6423
1994 7800 215 38 5975
1995 8100 216 33 6045
1996 7900 218 37 6123
1997 7850 217 34 6215
1998 8450 214 35 6187
1999 7900 216 36 6279
2000 8600 217 39 6386
2001 8850 216 40 6479
2002 8900 218 42 6332
2003 9150 217 36 6408

a. "Year" may be used as an x-variable.

b. The overall model is significant.

c. All x-variables are significant.

d. The coefficient of determination is greater than .7.

e. If we eliminate a variable, rainfall would be our first choice.