Question

Fund	3-year average return %	quality ranking	funk type	expense ratio %
1	14.39	1 star	GE	0.67
2	30.53	2 star	CB	1.41
3	3.34	3 star	FI	0.49
4	10.88	2 star	GE	0.99
5	11.32	1 star	GE	1.03
6	24.95	2 star	CB	1.23
7	15.67	2 star	GE	1.18
8	16.77	4 star	GE	1.31
9	18.14	3 star	GE	1.08
10	15.85	3 star	GE	1.20
11	17.25	2 star	GE	1.02
12	17.77	3 star	GE	1.32
13	17.23	2 star	GE	0.53
14	4.31	3 star	FI	0.44
15	18.23	4 star	GE	1.00

Run the regression model (use FI and 1-star as the reference categories for the categorical variables).

Generate a proper normal probability plot in the worksheet.

a. Type the estimated regression function.

b. What percentage of the total variability in 3-year average return is explained by the regression model?

c. What is the observed significance level of the estimated regression model?

d. Interpret the estimated regression coefficient for a 'GE' fund.

e. List and label each independent variables as: not significant (significance level > 0.1) or significant at the 0.1, 0.05, or 0.01 levels

f. State the 90% confidence interval for the coefficient of 'expense ratio'?

g. Predict the 3-year average return for a CB fund with a 3-star rating and an Expense ratio of 0.90% (report the final answer to one decimal place).

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression:

a) Regression equation:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.798428575
R Square	0.63748819
Adjusted R Square	0.538621333
Standard Error	4.644618793
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	3	417.2946523	139.0982174	6.447946335	0.008851963
Residual	11	237.2973211	21.57248373
Total	14	654.5919733
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 90.0%	Upper 90.0%
Intercept	-3.258866379	4.987746941	-0.653374443	0.526936189	-14.23682338	7.719090619	-12.21628539	5.698552631
quality ranking	3.682157254	3.889195132	0.946765881	0.364092419	-4.877903516	12.24221802	-3.30238924	10.66670375
fund type	9.895688408	5.198854352	1.903436361	0.0834635	-1.546912871	21.33828969	0.559144802	19.23223201
expense ratio %	7.315503496	5.809756686	1.259175537	0.234031208	-5.471684754	20.10269174	-3.118150337	17.74915733

a) 3-year average return % = -3.259 + 3.682*quality ranking + 9.986*fund type + 7.316*expense ratio%

b) Percentage of the total variability in 3-year average return is explained by the regression model: Adjusted R2 = 53.86%

c) Observed significance level of model: Significance F = 0.0089

d) Coefficient of  fund type = 9.986

If fund type is CB or FI, average return increases by 9.986 units and if its GE, it has no effect on average return.

e)

Variables	p-value	Significance at 0.1	Significance at 0.05	Significance at 0.01
quality ranking	0.364092419	Not Significant	Not Significant	Not Significant
fund type	0.0834635	Significant	Not Significant	Not Significant
expense ratio %	0.234031208	Not Significant	Not Significant	Not Significant

Since all the p-values are more than 0.1, 0.05 and 0.01, except for fund type at 0.1 level of significance, none of the variables are significant at any level of significance.

f) 90% confidence interval for the coefficient of 'expense ratio'

Lower limit = -3.118

Upper limit = 17.749

g) Prediction

Quality ranking: 3 star (1)

Fund type: CB (1)

Expense ratio = 0.90%

3-year average return % = -3.259 + 3.682*quality ranking + 9.986*fund type + 7.316*expense ratio%

= -3.259 + 3.682*1 + 9.986*1 + 7.316*0.90

= 16.99 ~ 17.0%