Question

Aron
	1	2	3	4	Average
8/6/2017	90	138	118	105	112.8
8/19/2017	162	101	120	145	132
9/16/2017	101	129	132	111	118.3
Average	117.7	122.7	123.3	120.3	121

Mjorgan
	1	2	3	4	Average
8/6/2017	115	88	94	102	99.8
8/19/2017	89	75	77	90	82.8
9/16/2017	74	110	117	90	97.8
Average	92.7	91	96	94	93.4

Mjorgan drinks a simple Egils beer while bowling. But Aron drinks the traditional Viking beverage Brennivín ("Black death") which has a particularly high alcohol content. As of his first game, he has not had any Brennivín, but after that he drinks about one per game bowled. Is there a correlation between his score and the number of Brennivín he has drank each night? (You might want to carefully construct a data table showing how many he has had at each point on each night, and his score. Note that three nights are presented here.) How would we interpret this correlation?

4. Could we write an equation to estimate Aron’s bowling score based on his Brennivín consumption? Run the statistical test to create this equation, diagnose it, and then interpret its findings and its accuracy. Is this a particularly good model?  

Answer 1

Yes, As per the data given for 3 nights, there is positive correlation between number of Brennivín and his score. However correlation is not very high. Out of 3 instances, one is showing negative correlation. Similarly if you can check the correlarion with average score of each drink, there is high positive correlation. Day 1 Day 2 Day 3 Average 1 90 162 101 118 2 138 101 129 123 3 118 120 132 123 4 105 145 111 120 Correlation 16% -15% 29% 44%

Days	Score	# of Brennivin
1	90	1
1	138	2
1	118	3
1	105	4
2	162	1
2	101	2
2	120	3
2	145	4
3	101	1
3	129	2
3	132	3
3	111	4
Score is dependent variable and # of Brennivin is independent variable. It is not a good model. R Square is just 4% it means that variablity in score is not completely explained by number of drinks. Again the p-value is very high. So we can conlcude that there might be another factors which are responsible for scores.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.048158058
R Square	0.002319199
Adjusted R Square	-0.097448882
Standard Error	22.01529771
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	11.26666667	11.26666667	0.023245898	0.881851741
Residual	10	4846.733333	484.6733333
Total	11	4858
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	118.8333333	15.5671663	7.633587965	1.77114E-05	84.14752543
# of Brennivin	0.866666667	5.684325427	0.152466054	0.881851741	-11.79879961
Equation -->	Score = 118.83 + number of Brennivin