A psychologist noted that people have more difficulty sleeping in a bright room

Question

A psychologist noted that people have more difficulty sleeping in a bright room than in a dark room. She measured whether the intensity of the light could predict the time it took a sample of 4 participants to fall asleep. The data for this hypothetical study are listed in the following table.

Intensity of
Light (in watts) Time It Took to
Sleep (in minutes)
X Y
5 13
10 21
20 32
40 37

Compute an analysis of regression for this hypothetical study. (Round your answers to two decimal places.)

reggression ss df ms fobt

error

total

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Y
Independent Variable: X
Y = 13.652174 + 0.64521739 X
Sample size: 4
R (correlation coefficient) = 0.92362601
R-sq = 0.853085
Estimate of error standard deviation: 5.075945

Parameter estimates:

Analysis of variance table for regression model:

Hence,

The ANOVA table will be:

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 13.652174 4.3639267 0 2 3.128415 0.0888 Slope 0.64521739 0.18933372 0 2 3.4078313 0.0764

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