ECON 438 Lecture Notes - Lecture 5: Dependent And Independent Variables, Analysis Of Variance, Coefficient Of Determination

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16 Jul 2020

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Managerial report: treating cost/mile as the dependent variable, develop an estimated regression with. Since the upscale sedan is highly correlated it has been removed from the equation. Cost/mile= 0. 665 0. 0233 * family sedan: treating value score as the dependent variable, develop an estimated regression equation using cost/mile, road-test score, predicted reliability, family-sedan, and upscale- Value score= 1. 24 2. 061 cost/mile + 0. 01 road test score + 0. 167 predicted reliability 0. 017. With an r square equal to 93. 31%: delete any independent variables that are not significant from the estimated regression equation developed in part 2 using a . 05 level of significance. After deleting any independent variables that are not significant, develop a new estimated regression equation. The size variable had a p value of 0. 45 which is greater than 0. 05 which mean that the variable is not significant to the equation. Value score= 1. 24 2. 043cost/mile + 0. 01 road test score + 0. 165 predicted reliability.

Related Questions

1. Write the subsequent demand equation, with Qd as the dependent variable; price, advertising, product development, and rel price as the independent variables.

2. How strong is the relationship between quantity demanded and the set of independent variables? List and explain 2 measures of this strength.

3. Which variable is most important in determining quantity demanded? Why?

Regression Statistics
Multiple R	0.655864641
R Square	0.430158427
Adjusted R Square	0.104534671
Standard Error	102678.3385
Observations	12

ANOVA
	df	SS	MS	F	Significance F
Regression	4	55709596185	13927399046	1.321029008	0.349980066
Residual	7	73799888386	10542841198
Total	11	1.29509E+11

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1422378.519	1185014.572	1.200304665	0.269060955	-1379735.677	4224492.715	-1379735.677	4224492.715
X Variable 1	-247037.6649	160481.181	-1.539355975	0.167610603	-626515.3574	132440.0276	-626515.3574	132440.0276
X Variable 2	0.081609431	1.398101115	0.058371623	0.955083996	-3.22437437	3.387593232	-3.22437437	3.387593232
X Variable 3	-1.015253706	3.150288749	-0.322273222	0.756657161	-8.46450288	6.433995469	-8.46450288	6.433995469
X Variable 4	177211.9244	145755.2053	1.215818838	0.263460235	-167444.3689	521868.2176	-167444.3689	521868.2176

*** Please see p. 2 for Question 2 ***

Question 2 (7 points)

The following Excel output shows the outcome of a linear regression of individuals%u2019 wage per hour (in dollars) on the number of years they attended school (in years).

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.381932619
R Square	0.145872525
Adjusted R Square	0.144267022
Standard Error	4.753758428
Observations	534

ANOVA
	df	SS	MS	F	Significance F
Regression	1	2053.22554	2053.22554	90.8578469	5.45998E-20
Residual	532	12022.25261	22.59821919
Total	533	14075.47815

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Upper 95.0%
Intercept	-0.745942699	1.045403804	-0.71354504	0.475821452	-2.799566599	1.307681201	1.307681201
Years of School	0.750448943	0.078729942	9.531938255	0.000545998	0.595789385	0.9051085	0.9051085

Part (a) (1 point)

What is the value of the estimated slope %u201Cb%u201D?

Part (b) (2 points)

Interpret the estimated value of the slope (i.e., explain what the number means in this regression).

Part (c) (1 point)

Is the estimate of the slope statistically significant? Please answer %u201Cyes%u201D or %u201Cno%u201D and explain how you can tell.

Part (d) (2 points)

Explain why we want to be able to reject the null hypothesis H0: %u03B2 = 0.

Part (e) (1 point)

How much of the total variation in wages can be explained by individuals%u2019 education?

correlation:

	medInc $	HS degree %
med inc	1
HS degree %	-0.033158666	1

regression:

multiple R	.03315867
R Square	.0010995
adjusted r sq	-.0177477
standard error	6902.6743
observation	55

	df	ss	ms	f	sig. f
regression	1	2779601.33	22779601.33	.05833749	.81007522
residual	53	2525286360	47646912.5
total	54	25280659

	coefficients	standard error	t stat	p-value	lower 95%	upper 95%	lower 95.0%	upper 95.0%
interpret	42273.3497	13809.7807	3.0611665	.00345814	14574.4373	69972.2621	14574.4373	69972.2621
hs degree	-49.414226	204.587042	-.2415316	.81007522	-459.76387	360.935414	-459.76386	360.935414

a. very briefly interpret the estimated correlation coefficient...the direction and strength of the correlation

b. List and label the dependent variable and independent variable

c. based on regression results if a country's percentage of the population with at least a high school diploma increases by 1 by how much and in one direction does a country's median income change?

d. what is the predicted medinc for an HS degree of 70%

e. what proportion of the variation in medinc is explained by our regression model explained by variation in HS degree?

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ECON 438 Lecture Notes - Lecture 5: Dependent And Independent Variables, Analysis Of Variance, Coefficient Of Determination

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