ECON 2P91 Assignment 1

Topics: Normal distribution, Standard deviation, Regression analysis Pages: 6 (728 words) Published: April 14, 2015


Assignment 1
1. Looking at SCORE variable, the skewness is -0.0511422 and excess kurtosis is 0.208336. For the normal distribution, skewness is zero. Since the skewness for SCORE variable is negative, this indicates that the distribution is skewed to the left (the long tail will be in the negative direction). For the normal distribution, kurtosis is three. So K-3 measures excess kurtosis. Since the excess kurtosis for SCORE variable is positive, the distribution is leptokurtic (it has thick tails as compared to the normal distribution. Summary Statistics, using the observations 1 - 324

for the variable SCORE (324 valid observations)
Mean
Median
Minimum
Maximum
1.70062
1.75000
0.500000
3.25000
Std. Dev.
C.V.
Skewness
Ex. kurtosis
0.522215
0.307074
-0.0511422
0.208336
5% Perc.
95% Perc.
IQ range
Missing obs.
0.750000
2.50000
0.500000
0
Summary Statistics, using the observations 1 - 324
for the variable PRICE (324 valid observations)
Mean
Median
Minimum
Maximum
21.6155
19.9199
9.90050
57.8035
Std. Dev.
C.V.
Skewness
Ex. kurtosis
6.49527
0.300492
1.34704
3.62715
5% Perc.
95% Perc.
IQ range
Missing obs.
13.2520
33.7187
7.50047
0

2. Using the scatterplot, SCORE and PRICE have upward trend or positive relationship.

3. The correlation coefficient (0.61115142) is positive and neither close to zero or one indicating a positive relationship (neither weak nor strong). Hence, an increase in wine quality score will cause an increase in price.

corr(PRICE, SCORE) = 0.61115142
Under the null hypothesis of no correlation:
t(322) = 13.8554, with two-tailed p-value 0.0000

4. Since the covariance of SCORE and PRICE (2.07298126) is positive, it indicates a positive relationship.

5. (i)
(ii) This model assumes that the direction of causation is from SCORE to PRICE.

6.
(0.975876) (0.548629)
Model 1: OLS, using observations 1-324
Dependent variable: PRICE

Coefficient
Std. Error
t-ratio
p-value

const
8.68833
0.975876
8.9031
7. The estimated intercept is 8.68833. When SCORE is equal to zero, the value of PRICE is 8.68833. However, this interpretation of the intercept not economically meaningful. The estimated slope is 7.60146. When SCORE increases by one unit, PRICE will increase by 7.60146 units. 8.

This algebraic fact indicates that the mean of the OLS residuals is always zero if the regression has an intercept. Observing the summary statistics below, we can confirm that the mean of the OLS residuals (-1.54993e-014) is essentially zero, when an intercept is included in the model.

Summary Statistics, using the observations 1 - 324
for the variable uhat1 (324 valid observations)
Mean
Median
Minimum
Maximum
-1.54993e-014
-0.331280
-13.7574
26.3108
Std. Dev.
C.V.
Skewness
Ex. kurtosis
5.14110
3.31700e+014
0.961424
2.96120
5% Perc.
95% Perc.
IQ range
Missing obs.
-7.18235
8.45773
6.63158
0

9.

5% Critical Value (2 sided test) = t-critical = 1.96
Since the absolute value of the t-ratio (13.86) exceeds the 5 percent critical value (1.96), we reject the null hypothesis and conclude that the slope coefficient is significantly different from zero.

10.

Therefore, p-value =
Since the level of significance (0.05) exceeds the p-value (0), we reject the null hypothesis and conclude that the slope coefficient is significantly different from zero. The answer is same as question 9.

11.
i.e. 6.526147 to 8.676773
Since the confidence interval does not include zero, it can be concluded that slope coefficient () is significantly different from zero. The answer is same as question 9 and 10.

12.

Therefore, using the estimated regression, the predicted price of that wine is $23.89.

13. The coefficient of determination () is 0.373506. indicates the percentage of variation in dependent variable...
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