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Eduardwww [97]
3 years ago
11

PLZ RESPOND ASAP HELPPPP

Mathematics
1 answer:
Ronch [10]3 years ago
3 0

The question is the thing that needs help. What does that hanging "a leading 2" mean? And rational real coefficients? Obviously if they're rational they're gonna be real, but really.


I would say "a leading 2" means the highest power of x has a coefficient to two, which is none of the above.


The last two are of degree two, which is the lowest degree. They both have integer coefficients, so are necessarily real and rational as well.


Neither has a leading 2 as far as I can tell. The last one is monic (a leading coefficient of 1). I like monic polynomials so I'd pick that one, but that doesn't make it right.


None of the above



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Answer:

1)  \hat \beta_1 =\frac{466}{234}=1.991

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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"  

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Data given

n=10 \sum (x-\bar x)(y-\bar y) =466,\sum (x-\bar x)^2 =234 , \sum(y-\bar y)^2 =1434  

Part 1

The slope is given by this formula:

\hat \beta_1 =\frac{\sum (x-\bar x) (y-\bar y)}{\sum (x-\bar x )^2}

If we replace we got:

\hat \beta_1 =\frac{466}{234}=1.991

Part 2

We can find the intercept with the following formula

\hat \beta_o = \bar y -\hat \beta_1 \bar x

We can find the average for x and y like this:

\bar X=90/10 = 9. \bar y= 170/9=18.89

And replacing we got:

\hat \beta_o = 18.89 -1.991 (9)=0.970

Part 3

For this case we have the SSE=505.98 who represent the sum of squares for the error.

The total sum of squares is given by SST \sum (y-\bar y)^2 = 1434

And since the total variation is the sum of squares for the regression and the error we have this:

SST= SSR+SSE

And solving for SSR we got:

SSR= SST-SSE= 1434-505.98=928.02

Part 4

In order to calculate the correlation coefficient we can use this formula:  

r=\frac{\sum (x-\bar x)(y-\bar y) }{\sqrt{[\sum (x-\bar x)^2][\sum(y-\bar y)^2]}}  

For our case we have this:  

n=10 \sum (x-\bar x)(y-\bar y) =466,\sum (x-\bar x)^2 =234 , \sum(y-\bar y)^2 =1434  

So we can find the correlation coefficient replacing like this:

r=\frac{466}{\sqrt{[234][\sum(1434]}}=0.804

And the determination coeffecient is r^2 = 0.804^2 =0.647  

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