Human Interaction And Problem solving

RegressionPracticewithANSWERS.xlsx

Problem 1

Training	Profit	Is there a relationship between hours of training and amount of profit per employee?
2	75
3	65
4	76
5	54
1	75
2	49
3	30
4	49
5	30
6	40
1	50
2	20
3	40
4	60
5	70
6	40

Training	Profit	Is there a relationship between hours of training and amount of profit per employee?
2	75
3	65	SUMMARY OUTPUT
4	76
5	54	Regression Statistics				There is no relationship between hours of training and amount of profit per employee
1	75	Multiple R	0.1683601193			(r [14] = .17, p > .05).
2	49	R Square	0.0283451298			Notice that running the regression and looking at the multiple r, or looking at the Pearson on the t-test give you the same correlation.
3	30	Adjusted R Square	-0.0410587895			Remember, the df for the regression/Pearson is N-2.					t-Test: Paired Two Sample for Means
4	49	Standard Error	1.666180294
5	30	Observations	16									Training	Profit
6	40										Mean	3.5	51.4375
1	50	ANOVA									Variance	2.6666666667	309.0625
2	20		df	SS	MS	F	Significance F				Observations	16	16
3	40	Regression	1	1.1338051904	1.1338051904	0.4084082001	0.5330957594				Pearson Correlation	-0.1683601193
4	60	Residual	14	38.8661948096	2.7761567721						Hypothesized Mean Difference	0
5	70	Total	15	40							df	15
6	40										t Stat	-10.6958487157
			Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%	P(T<=t) one-tail	0.0000000102
		Intercept	4.3044152342	1.3258636777	3.2464990984	0.005853328	1.4607204684	7.1481100001	1.4607204684	7.1481100001	t Critical one-tail	1.7530503557
		Profit	-0.0156386923	0.024471084	-0.639068228	0.5330957594	-0.0681239475	0.0368465629	-0.0681239475	0.0368465629	P(T<=t) two-tail	0.0000000205
											t Critical two-tail	2.1314495456

Practice	Score	Is there a relationship between the amount of time that students practice statistics and their exam score?
2	60
3	70
4	80
5	90
6	90
7	95
8	97
9	98
10	99
10	100

Practice	Score	Is there a relationship between the amount of time that students practice statistics and their exam score?
2	60										t-Test: Paired Two Sample for Means
3	70	SUMMARY OUTPUT		There is a relationship between amount of time practicing statistics and
4	80			student performance, (r [8] = .93, p < .01).								Practice	Score
5	90	Regression Statistics									Mean	6.4	87.9
6	90	Multiple R	0.9274655051								Variance	8.2666666667	186.1
7	95	R Square	0.8601922631								Observations	10	10
8	97	Adjusted R Square	0.842716296								Pearson Correlation	0.9274655051
9	98	Standard Error	1.1402683688								Hypothesized Mean Difference	0
10	99	Observations	10								df	9
10	100										t Stat	-23.370660174
		ANOVA									P(T<=t) one-tail	0.0000000011
			df	SS	MS	F	Significance F				t Critical one-tail	1.8331129327
		Regression	1	63.9983043764	63.9983043764	49.2214398053	0.0001108777				P(T<=t) two-tail	0.0000000023
		Residual	8	10.4016956236	1.300211953						t Critical two-tail	2.2621571628
		Total	9	74.4
			Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
		Intercept	-10.782195952	2.4754744376	-4.3556078739	0.0024269198	-16.4906502417	-5.0737416623	-16.4906502417	-5.0737416623
		Score	0.1954743567	0.0278620223	7.0157992991	0.0001108777	0.131224418	0.2597242954	0.131224418	0.2597242954