Chi - Squared and Anova I was provided with the solutions or what the problem sh
ID: 3182639 • Letter: C
Question
Chi - Squared and Anova
I was provided with the solutions or what the problem should solve to but still lost. Please help. Thank you!
Ull, llse the data to estirate izs 20. The following data refer to the number of deaths per 10,000 adults in a large Eastern city in the different seasons for the years 1982 to 1986. Year Winter Spring Summer Fall 1982 33.6 31.4 29.8 32.1 1983 32.5 30.1 28.5 29.9 1984 35.3 33.2 29.5 28.7 1985 34.4 28.6 33.9 30.1 1986 37.3 34.1 28.5 29.4 (a) Assuming a two-factor model, estimate the parameters. (b) Test the hypothesis that death rates do not depend on the season. Use the 5 percent level of significance. (c) Test, at the 5 percent level of significance, the hypothesis that there is no effect due to the year.Explanation / Answer
Answer:
MINITAB USED:
a).
Regression Equation
deaths = 31.545 + 0.180 year_1982 - 1.295 year_1983 + 0.130 year_1984 + 0.205 year_1985 + 0.780 year_1986 - 1.505 season_fall - 0.065 season_spring - 1.505 season_summer + 3.075 season_winter
b).
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
year 4 9.507 2.377 0.57 0.691
season 3 69.949 23.316 5.57 0.012
Error 12 50.213 4.184
Total 19 129.669
To test season effect, calculated F=5.57, P=0.012 which is < 0.05 level of significance.
Ho is Rejected.
Season effect is significant.
c).
To test year effect, calculated F=0.57, P=0.691 which is > 0.05 level of significance.
Ho is Not Rejected.
Year effect is not significant.
General Linear Model: deaths versus year, season
Method
Factor coding (-1, 0, +1)
Factor Information
Factor Type Levels Values
year Fixed 5 1982, 1983, 1984, 1985, 1986
season Fixed 4 fall, spring, summer, winter
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
year 4 9.507 2.377 0.57 0.691
season 3 69.949 23.316 5.57 0.012
Error 12 50.213 4.184
Total 19 129.669
Model Summary
S R-sq R-sq(adj) R-sq(pred)
2.04558 61.28% 38.69% 0.00%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 31.545 0.457 68.96 0.000
year
1982 0.180 0.915 0.20 0.847 1.60
1983 -1.295 0.915 -1.42 0.182 1.60
1984 0.130 0.915 0.14 0.889 1.60
1985 0.205 0.915 0.22 0.826 1.60
season
fall -1.505 0.792 -1.90 0.082 1.50
spring -0.065 0.792 -0.08 0.936 1.50
summer -1.505 0.792 -1.90 0.082 1.50
Regression Equation
deaths = 31.545 + 0.180 year_1982 - 1.295 year_1983 + 0.130 year_1984 + 0.205 year_1985 + 0.780 year_1986 - 1.505 season_fall - 0.065 season_spring - 1.505 season_summer + 3.075 season_winter
Fits and Diagnostics for Unusual Observations
Std
Obs deaths Fit Resid Resid
14 33.90 30.25 3.65 2.31 R
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