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 Time It Took to Light (in watts) Sleep (in minutes) 10 16 20 29 35 Compute an analysis of regression for this hypothetical study. (Round your answers to two decimal places.) Source of MS SS Variation 369 x 369 x 18 x Regression Residual (error) 40.99 X 2 20.5 x 410 x 3 Total

Explanation / Answer

Solution:

Here, we have to complete the ANOVA table for the regression. The formulas for completing these values of ANOVA table are given as below:

SST = SSR + SSE

df for total = n – 1

df for regression = c – 1 where c is number of variables

Here, there are two variables, c = 2, so df for regression = 2 – 1 = 1

Total number of observations = n = 4

So, df for total = 4 – 1 = 3

df for error = df for total – df for regression = 3 – 1 = 2

MSR = SSR/dfregression

MSE = SSE/dferror

Fobt = MSR/MSE

By using these formulas, the ANOVA table is given as below:

Source of variation

SS

df

MS

Fobt

Regression

390.8174

1

390.8174/1 = 390.8174

390.8174 / 29.5913 = 13.20717

Residual

59.18261

2

59.18261/2 = 29.5913

Total

450

3

Source of variation

SS

df

MS

Fobt

Regression

390.8174

1

390.8174/1 = 390.8174

390.8174 / 29.5913 = 13.20717

Residual

59.18261

2

59.18261/2 = 29.5913

Total

450

3

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.