Complete Question
The complete question is shown on the first uploaded image
Answer:
a
SST = 1800
SSR = 1512.376
SSE = 287.624
b
coefficient of determination is [tex]r^2 \approx 0.8402[/tex]
What this is telling us is that 84.02% variation in dependent variable y can be fully explained by variation in the independent variable x
c
The correlation coefficient is [tex]r = 0.917[/tex]
Step-by-step explanation:
The table shown the calculated mean is shown on the second uploaded image
Let first define some term
SST (sum of squares total) : This is the difference between the noted dependent variable and the mean of this noted dependent variable
SSR(sum of squared residuals) : this can defined as a predicted shift from the actual observed values of the data
SSE (sum of squared estimate of errors): this can be defined as the sum of the square difference between the observed value and its mean
From the table
[tex]SST = SS_{yy} = 1800[/tex]
[tex]SSR = \frac{SS^2_{xy}}{SS_{xx}} = \frac{4755^2}{14950} = 1512.376[/tex]
[tex]SSE =SST-SSR[/tex]
[tex]=1800 - 1512.376[/tex]
[tex]= 287.62[/tex]
The coefficient of determination is mathematically represented as
[tex]r^2 = \frac{SSR}{SST}[/tex]
[tex]= 1-\frac{SSE}{SST}[/tex]
[tex]r^2= 1-\frac{287.6237}{1800}[/tex]
[tex]r^2 \approx 0.8402[/tex]
The correlation coefficient is mathematically represented as
[tex]r = \pm\sqrt{r^2}[/tex]
Substituting values
[tex]r = \sqrt{0.84020}[/tex]
[tex]r = 0.917[/tex]
this value is + because the value of the coefficient of x in estimated regression equation([tex]24.9 + 0.301x,[/tex]) is positive
