Respuesta :
Answer:
[tex]R^2 = \frac{SSE}{SST}=\frac{1009.45}{1105.64}=0.913[/tex]
And from the definition of determination coeffcient we know that this value represent the % of variance explained by the linear model so on this case 0.913*100=91.30% of the vraince explained by the model.
C. 91.30%
Step-by-step explanation:
Previous concepts
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1. And is defined as:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.
Solution to the problem
For this case we have the SSE=1009.45 who represent the sum of squares for the error.
The total sum of squares is given by [tex]SST \sum (y-\bar y)^2 = 1105.64[/tex]
And since the total variation is the sum of squares for the regression and the error we have this:
[tex]SST= SSR+SSE[/tex]
And solving for SSR we got:
[tex]SSR= SST-SSE= 1105.64-1009.45=96.19[/tex]
The determination coefficient when we conduct a multiple regression is defined as:
[tex]R^2 = \frac{SSE}{SST}=\frac{1009.45}{1105.64}=0.913[/tex]
And from the definition of determination coeffcient we know that this value represent the % of variance explained by the linear model so on this case 0.913*100=91.30% of the vraince explained by the model.
C. 91.30%
