Show that the value of the expression: ( 10+5 3 + 10−5 3 )2 is a rational number.
1 answer:
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Answer:
a)
b) Figure attached
c)
Step-by-step explanation:
We assume that th data is this one:
x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90
y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.
a) Find the least-squares line appropriate for this data.
For this case we need to calculate the slope with the following formula:
Where:
So we can find the sums like this:
With these we can find the sums:
And the slope would be:
Nowe we can find the means for x and y like this:
And we can find the intercept using this:
So the line would be given by:
b) Plot the points and graph the line as a check on your calculations.
For this case we can use excel and we got the figure attached as the result.
c) Calculate S^2
In oder to calculate S^2 we need to calculate the MSE, or the mean square error. And is given by this formula:
The degred of freedom for the error are given by:
We can calculate:
And now we can calculate the sum of squares for the regression given by:
We have that SST= SSR+SSE, and then SSE=SST-SSR= 792-601.67=190.33[/tex]
So then :
