The klein corporations marketing department, using regression analysis estimated

Question

The klein corporations marketing department, using regression analysis estimated the firms demand function. The result of this estimation was: Q=-104 -2.1P +3.2I +1.5A +1.6Z Where Q is the quantity demanded of the firms product (in tons), P is the price of hte firms product (in dollars per ton), I is the per capita income (in dollars) , A is the firms advertising expenditure (in thousands of dollars), and Z is the price (in dollars) of a competing product. Are any of the estimated coefficients not statistically differnt from zero at hte 95% level of confidence? if so which ones? and What proportio of the variation is the quantities demanded is not explained by this regression equation?

the standar erro of regression are -104 is 21 -2.1P is .12 3.2I is 1.1 1.5A is .21 and 1.6Z is .72

R2 =.89 and Standrad error of estimae = 108

Is this the info you were needing?

Explanation / Answer

We say a variable is statistically significant if the observed t value doesn't lie in the acceptance region. Because if we are in the acceptance region that means that we are accepting the null hypothesis which says that the variable is insignificant.

For the Constant, t = (-104)/21 = 4.95. This value lies in the rejection region, where we don't accept the null hypothesis. So that means, Constant is significant.

For the Price's Coefficient, t = (-2.1)/(.12) = 17.5. This value is also way far from the acceptance region, so this coefficient is also significant.

Similarly, in this fashion, we will calculate the t values of the rest of the variables. And here ONE THING IS MISSING AND THAT IS NUMBER OF TERMS. So this information is missing.

So, if we assume the degrees of freedom then for some the coefficient of I and Z are not significant and for some they are. But rest is always significant.

Here R^2 is 0.89, that means 89% of the variation is jointly explained by all these variables.

So, the remaining 11% has not been explained by these variables.

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