Answer to Question #261670 in Accounting for Muller

Question

The following data refers to the price of a good ‘P’ and the quantity of the good supplied,

‘S’.

P 2 7 5 1 4 8 2 8

S 15 41 32 9 28 43 17 40

a. Estimate the linear regression line (S)   P

b. Estimate the standard errors of ˆ and ˆ

c. Test the hypothesis that price influences supply

d. Obtain a 95% confidence interval for 

Answer 1

a. Linear Regression Line:

Following is the output of linear regression between price and quantity supplied:

E(S ) = a + bP

E(S) = 6.9866 + 4.5705P

b. Standard Errors:

standard error (SE) of coefficient a = 1.7861

standard error (SE) of coefficient b = 0.3353

c. Hypothesis Testing:

As shown in above output, slope coefficient is 4.5705. This tells that the average value of quantity supplied increases by 4.5705 on average for additional price of a good.

It is also found that F value is greater than critical value (185.8017 > 0.0000), so null hypothesis can be rejected.

P-value is also less than level of significance (0.0000 < 0.05) that also supports this finding.

Based on this, it can be concluded that price of a good influences its supply in the market.

d. Confidence Interval:

A 95% confidence interval for coefficient a is 2.6162 to 11.3570.