Question

Hi,

Im doing my final project for quanatative analysis class. I was tasked to create a regression analysis on Does the number of probowl player have bearing on becoming all pro. I ran the regression for the following data and got this output from Megastat but I'm not sure what it tells me.

Regression Analysis
	r²	0.006	n	239
	r	0.076	k	1
	Std. Error	0.494	Dep. Var.	All Pro
ANOVA table
Source	SS	df	MS	F	p-value
Regression	0.3397	1	0.3397	1.39	.2392
Residual	57.8193	237	0.2440
Total	58.1590	238
Regression output					confidence interval
variables	coefficients	std. error	t (df=237)	p-value	95% lower	95% upper
Intercept	-0.1681	0.4981	-0.337	.7361	-1.1493	0.8131
Pro Bowl	0.5840	0.4950	1.180	.2392	-0.3911	1.5591

Sum of Pro Bowl Count	Sum of All Pro Count
240	101

Answer 1

The above results showed if the number of pro bowl players has a bearing on becoming all pro, dependent variable being all pro and independent being- number of pro bowl players.

Firstly, the value of R2 , which is the coefficient of determination, shows the degree to which all the independent variables explain the variation in the dependent variable. Here, R2 has a value- 0.006 i.e. 0.6%. This is the percentage to which number of pro bowl players impact all pro, which is extremely low. This shows that there is a huge possibility that there are other variables that have an impact on the dependent variable which are not included in the model.
The value of r is the correlation coefficient signifying the degree of association between the two variables which in this case is 0.076, this value is low and positive. Another thing to be noted to show the direction of the relation of the two variables is coefficient value of pro bowl under the regression output- 0.5840, again a positive value signifying positive relationship between the two.

The coefficient of pro bowl actually shows that with an increase in the number of pro bowl players by 1, the all pro increases by 0.5%.

Looking at the p-value of f-stat, which is 0.2392 and is quite high. This reveals that the test is not statistically significant or reliable to be able to be used to draw further conclusions.