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

<0.00001

***

SCORE

7.60146