Question

1) A psychologist is investigating the relationship between drinking coffee and sleep. She chooses 20 participants and measures how many cups of coffee they had the previous day and how many hours of sleep they got the night before. The data is presented below:

Coffee	Sleep
0	9.5
1	9.5
4	7
5	6
2	8
3	8.5
1	8
1	6
4	6
3	7
6	7
6	7.5
2	8.5
0	9
1	9
2	7
4	5
3	6
5	7
7	6

For this data you will:

• Use the SPSS program to calculate the correlation and create a scatterplot
• Provide the appropriate output
• How would you describe this relationship? (both strength and direction, and in layman’s terms)
• Are these variables truly related or could there be a third variable at play?
• Calculate the regression equation (show your work)
• How much sleep should someone get if they drink 5 cups of coffee in a day?
• Calculate the proportionate reduction in error

Answer 1

Correlation Matrix:

	Coffee	Sleep
Coffee	1
Sleep	-0.62067	1

Thee value of r in this case (r = -0.62067) indicates that there is a negative, linear relationship of moderate strength between Coffee and Sleep.

Yes, there could be a confounding variable like Stress which is inducing more coffee intake and less sleep simultaneously.

Regression Output:

Regression Statistics
Multiple R	0.620668258
R Square	0.385229086
Adjusted R Square	0.351075146
Standard Error	1.068654461
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	12.88109756	12.88109756	11.27919911	0.003498911
Residual	18	20.55640244	1.142022358
Total	19	33.4375
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	8.56402439	0.427135851	20.04988429	9.22673E-14	7.666645267	9.461403514	7.666645267	9.461403514
Coffee	-0.396341463	0.118013143	-3.358451892	0.003498911	-0.644277877	-0.14840505	-0.644277877	-0.14840505

Regression Equation:

Sleep = 8.564 - 0.396*coffee

If coffee cups = 5

Sleep = 8.564 - 0.396*5

= 6.584 hrs

proportionate reduction in error = Coefficient of Determination = R² = r²

= 0.385

i.e. moderate

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