Sherwin-Williams Company is attempting to develop a demand model for its line of

Question

Sherwin-Williams Company is attempting to develop a demand model for its line of exterior house paints. The company’s chief economist feels that the most important variables affecting paint sales (y) (measured in thousand gallons) are

Promotional expenditure (a) (measured in thousand dollars)

Selling price (p) (measured in dollars per gallon)

Disposable income per household (m) (measured in thousand dollars).

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logy|       Coefficient      Std. Err.        t         P>|t|    [95% Conf. Interval]

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loga -.0232291    .1420415    -0.16     0.875    -.3707923     .324334

logp -1.037375     .3655166    -2.84     0.030    -1.931762   -.1429884

logm .3882373    .3753380     1.03      0.341    -.5301816    1.306656

constant |   6.951867    1.442853      4.82     0.003     3.421333     10.4824

First conduct an appropriate t-test for each independent variable except the constant as to whether it is statistically significant at the 95% confidence level, and then make an economic interpretation of each of the statistically significant coefficients. Use the “Students” probability distribution table for two-tailed tests (data set 30 observations as noted above)

Explanation / Answer

At 95% significant level if t value is higher than 2 then that parameter is statistcally significant and we can reject the nulll hypothesis

T value=Coefficient Estimate/Std.Error

For Log(Selling Price) we have t highr than 2 and for loga & logm it is not significant because it is less than 2

SImilarly constant also has staistcially significant t value therefore there is no harm in excluding log a and log m from this model

Interpretation can be given irrespective of any change in level of price LogY will be always equal to 6.951867

If Price changes by 1% then Production changes by 1.037% in opposite direction due to negative sign

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