The table shows the distances and times that four rowboats traveled. Which rowboat was the fastest?
1 answer:
You might be interested in
Answer:
Check the explanation below and the attached files.
Step-by-step explanation:
Hello!
With the given information you need to develop an ANOVA table for the regression analysis, with variables X: hours studied as predictor and Y: grade earned on the first statistic exam as the dependent variable.
The ANOVA table in the first attached file shows in a general way each element of it and how they are calculated.
The information you have is:
Sample n= 26
Se= 12 ⇒ Se²= 144
R²= 0.80
Number of independent variables k= 1
First: The easiest step is to calculate the degrees of freedom
Degrees of freedom of the treatment (regression) DfTr= k= 1
Degrees of freedom of the residual DfE= n - 2 = 26 - 2 = 24
Degrees of freedom of the totals DfT= n - 1 = 26 - 1 = 25
To calculate the Square Sums you have to use the values of Se and R²
The sample variance of the residues (Se²) (also the Mean Square of Residues) and you calculate it as the Sum Square of residues divided the degrees of freedom of the residues.
Se²= MSE = SSE/DfE
SSE= MSE * DfE = 144*24= 3456
The coefficient of determination is calculated as the division between the Square Sum of treatment and the Square Sum of the Totals.
R²= SStr/SST ⇒ SStr= R² * SST (1)
And the Sum of Squares of the Total is the sum of the Sum of Squares of the tratment and the Sum of Squares of the resudues.
(2) SST = SStr + SSE
Using a doble equation system, replacin (1) in (2):
SST = SStr + SSE ⇒ SST = (R² * SST) + SSE
SST - 0.8*SST= SSE
0.2*SST = SSE
SST = SSE/0.2 = 3456/0.2
SST = 17280
Then:
SStr= R² * SST = 0.8 * 17280
SStr= 13824
Now the only elements of the table that are left are the MSTr and the velue of the Statistic.
MSTr= SStr/DfTr= 13824/1 = 13824
F= MStr/MSE = 13824/144 = 96
Check the 2nd attachment, I've summarized all calculation into the table.
I hope it helps!
