Question

(2)The data set below gives the quantity of output supplied by a firm (Q) at various prices (P) over a

14-month period.

Month 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Q 98 100 103 105 80 87 94 113 116 118 121 123 126 128

P 0.79 0.80 0.82 0.82 0.93 0.95 0.96 0.88 0.88 0.90 0.93 0.94 0.96 0.97

The firm faced a STRIKE by its workers in the 5th, 6th, and 7th months.

Given the information above

(a)Write a regression model for the firm’s production function which includes the “variable” that represents the impact of the strike on production.

(b)Explain the value this “variable” can assume in this model.

(c)Suppose the estimated coefficient for this variable is (– 37.64) with a standard error ( Se) of

(-23.59) can you say the strike had a significant impact on production ? Conduct an appropriate statistical test at the 5% level of significance.

Answer 1

(a)

Assume the variable is Strike that takes the value of 1 for 5th, 6th, and 7th months

Dependent variable = Q

Independent variables = P and Strike

The regression model is:

Month	Q	P	Strike		SUMMARY OUTPUT
1	98	0.79	0
2	100	0.8	0		Regression Statistics
3	103	0.82	0		Multiple R	0.99083178
4	105	0.82	0		R Square	0.981747617
5	80	0.93	1		Adjusted R Square	0.978429001
6	87	0.95	1		Standard Error	2.203436857
7	94	0.96	1		Observations	14
8	113	0.88	0
9	116	0.88	0		ANOVA
10	118	0.9	0			df	SS	MS	F	Significance F
11	121	0.93	0		Regression	2	2872.593526	1436.296763	295.8305102	2.73689E-10
12	123	0.94	0		Residual	11	53.40647381	4.855133983
13	126	0.96	0		Total	13	2926
14	128	0.97	0
						Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
					Intercept	-32.47444179	9.366952086	-3.466916612	0.005268524	-53.09096433	-11.85791926	-53.09096433	-11.85791926
					P	165.9668586	10.60649982	15.64765582	7.29773E-09	142.6221099	189.3116073	142.6221099	189.3116073
					Strike	-37.640851	1.59568201	-23.58919307	0.000000000	-41.15292343	-34.12877858	-41.15292343	-34.12877858

The regression equation is: Q = -32.4744417918832 + 165.966858587277*P -37.6408510040725*Strike

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(b)

The variable Strike takes the value of 1 for 5th, 6th, and 7th months, indicating that strike occurred in those months and takes a value of 0 for the other months.

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(c)

The estimated coefficient of the variable Strike is -37.64

Mistakenly, in the question, the standard error is stated as -23.59

-23.59 is the value of t-statistic of the coefficient of the variable Strike (See table for regression result above - highlighted in amber color)

The absolute value of the t-statistic is 23.59, which is quite higher than the critical t-statistic at a 5% level of significance.

Collararily, the p-value is 9.03726709329411E-11, which is lower than the critical p-value of 0.05 at a 5% level of significance.

This means, the variable Strike is statistically significant at a 5% level of significance.

Hence, one can conclude that the strike had a significant impact on production