Question

One of the theories regarding initial public offering (IPO) pricing is that the initial return y(the percentage change from offer to open price) on an IPO depends on the price revision x (the percentage change from pre-offer to offer price). Another factor that may influence the initial return is a high-tech dummy variable that equals 1 for high-tech firms and 0 otherwise. The following table shows a portion of the data on 264 IPO firms from January 2001 through September 2004.

Initial Return	Price Revision	High-Tech
36.42	11.55	0
19.51	−23.11	0
⋮	⋮	⋮
-2.67	−24.50	1

a-1. Estimate y = β_o + β₁x + β₂d + ε where the dummy variable d equals 1 for firms that are high-tech. (Round your answers to 2 decimal places.)

initial return =  +  Price Revision +  High-Tech

a-2. Use the estimated model to predict the initial return of a high-tech firm with a 10% price revision. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

a-3.  Find the corresponding predicted return of a firm that is not high-tech. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

b-1. Estimate y = β_o + β₁x + β₂d + ε where the dummy variable d equals 1 for firms that are not high-tech. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal place.)

initial return =  +  Price Revision +  High-Tech

b-2. Use the estimated model to predict the initial return of a high-tech firm with a 10% price revision. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.

b-3. Find the corresponding predicted return of a firm that is not high-tech. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

c-1. In the high-tech models, determine if the dummy variable is significant at the 5% level.

• The dummy variable is significant since the p-value is less than 0.05.

• The dummy variable is not significant since the p-value is more than 0.05.

• The dummy variable is significant since the p-value is more than 0.05.

• The dummy variable is not significant since the p-value is less than 0.05.

c-2. In the not high-tech models, determine if the dummy variable is significant at the 5% level.

• The dummy variable is significant since the p-value is less than 0.05.

• The dummy variable is not significant since the p-value is more than 0.05.

• The dummy variable is significant since the p-value is more than 0.05.

• The dummy variable is not significant since the p-value is less than 0.05.

Answer 1

Excel > Data > Data Analysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.405989
R Square	0.164827
Adjusted R Square	0.158427
Standard Error	10.28656
Observations	264
ANOVA
	df	SS	MS	F	Significance F
Regression	2	5450.464786	2725.232393	25.75510175	6.19167E-11
Residual	261	27617.27216	105.8133033
Total	263	33067.73694
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	8.447866	0.816497569	10.34646841	3.00791E-21	6.840105244	10.05562735	6.840105244	10.05562735
Price Revision	0.228575	0.032754836	6.978353202	2.45872E-11	0.164077439	0.293072188	0.164077439	0.293072188
High-tech	3.984711	1.323503695	3.010729363	0.002861666	1.378607294	6.59081558	1.378607294	6.59081558

a1)

Initial return = 8.45 + 0.23 * Price Revision + 3.98 * High-Tech

a2)

the estimated model to predict the initial return of a high-tech firm with a 10% price revision

Price revision = 0.1

High-Tech = 1

Initial return = 8.4479 + 0.2286 * Price Revision + 3.9847 * High-Tech

Initial return = 8.4479 + 0.2286 * 0.1 + 3.9847 * 1 = 12.46

a3)

the corresponding predicted return of a firm that is not high-tech

Price revision = 0.1

High-Tech = 0

Initial return = 8.4479 + 0.2286 * Price Revision + 3.9847 * High-Tech

Initial return = 8.4479 + 0.2286 * 0.1 + 3.9847 * 0 = 8.47

b1)

Change dummy variables 0 as 1 and 1 as 0

Excel > Data > Data Analysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.405989248
R Square	0.164827269
Adjusted R Square	0.158427478
Standard Error	10.28655935
Observations	264
ANOVA
	df	SS	MS	F	Significance F
Regression	2	5450.464786	2725.232393	25.75510175	6.19167E-11
Residual	261	27617.27216	105.8133033
Total	263	33067.73694
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	12.43257774	1.074351532	11.57216922	2.83614E-25	10.3170778	14.54807767	10.3170778	14.54807767
Price Revision	0.228574814	0.032754836	6.978353202	2.45872E-11	0.164077439	0.293072188	0.164077439	0.293072188
High-tech	-3.984711437	1.323503695	-3.010729363	0.002861666	-6.59081558	-1.378607294	-6.59081558	-1.378607294

Initial return = 12.43 + 0.23 * Price Revision - 3.98 * High-Tech

b2)

the estimated model to predict the initial return of a high-tech firm with a 10% price revision

Price Revision = 0.1

High-Tech = 0

Initial return = 12.4326 + 0.2286 * Price Revision - 3.9847 * High-Tech

Initial return = 12.4326 + 0.2286 * 0.1 - 3.9847 * 0 = 12.46

b3)

the corresponding predicted return of a firm that is not high-tech

Price Revision = 0.1

High-Tech = 1

Initial return = 12.4326 + 0.2286 * Price Revision - 3.9847 * High-Tech

Initial return = 12.4326 + 0.2286 * 0.1 - 3.9847 * 1 = 8.47

c1)

P value = 0.0029

The dummy variable is significant since the p-value is less than 0.05.

c2)

P value = 0.0029

The dummy variable is significant since the p-value is less than 0.05.