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borishaifa [10]
3 years ago
15

Pleaseeeeeee help meeeeeeeeeee

Mathematics
1 answer:
vladimir1956 [14]3 years ago
8 0
The answer is -10u you add and subtract the like terms
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Consider the simple linear regression model Yi=β0+β1xi+ϵi, where ϵi's are independent N(0,σ2) random variables. Therefore, Yi is
Virty [35]

Answer:

See proof below.

Step-by-step explanation:

If we assume the following linear model:

y = \beta_o + \beta_1 X +\epsilon

And if we have n sets of paired observations (x_i, y_i) , i =1,2,...,n the model can be written like this:

y_i = \beta_o +\beta_1 x_i + \epsilon_i , i =1,2,...,n

And using the least squares procedure gives to us the following least squares estimates b_o for \beta_o and b_1 for \beta_1  :

b_o = \bar y - b_1 \bar x

b_1 = \frac{s_{xy}}{s_xx}

Where:

s_{xy} =\sum_{i=1}^n (x_i -\bar x) (y-\bar y)

s_{xx} =\sum_{i=1}^n (x_i -\bar x)^2

Then \beta_1 is a random variable and the estimated value is b_1. We can express this estimator like this:

b_1 = \sum_{i=1}^n a_i y_i

Where a_i =\frac{(x_i -\bar x)}{s_{xx}} and if we see careful we notice that \sum_{i=1}^n a_i =0 and \sum_{i=1}^n a_i x_i =1

So then when we find the expected value we got:

E(b_1) = \sum_{i=1}^n a_i E(y_i)

E(b_1) = \sum_{i=1}^n a_i (\beta_o +\beta_1 x_i)

E(b_1) = \sum_{i=1}^n a_i \beta_o + \beta_1 a_i x_i

E(b_1) = \beta_1 \sum_{i=1}^n a_i x_i = \beta_1

And as we can see b_1 is an unbiased estimator for \beta_1

In order to find the variance for the estimator b_1 we have this:

Var(b_1) = \sum_{i=1}^n a_i^2 Var(y_i) +\sum_i \sum_{j \neq i} a_i a_j Cov (y_i, y_j)

And we can assume that Cov(y_i,y_j) =0 since the observations are assumed independent, then we have this:

Var (b_1) =\sigma^2 \frac{\sum_{i=1}^n (x_i -\bar x)^2}{s^2_{xx}}

And if we simplify we got:

Var(b_1) = \frac{\sigma^2 s_{xx}}{s^2_{xx}} = \frac{\sigma^2}{s_{xx}}

And with this we complete the proof required.

8 0
4 years ago
Use perfect square factoring patterns<br> y^2 + 16y + 64 = 0
Pepsi [2]

Arrange your given equation to resembles the form
a^2 +2ab+ b^2 because this equals (a+b)^2

So we get:
y^2+16y+8^2=0

Now compare
y^2+16y+8^2 to a^2 +2ab+ b^2

So we got
y^2+2•8 y+8^2=0 which equals (y+8)^2






8 0
4 years ago
The length of a rectangle is 4cm greater than its width. the perimeter is 32 cm. find the length of the rectangle.
lord [1]

The correct answer should be 12!

3 0
3 years ago
PLZZ HELP!?!?Graph the linear equation −5x+y=−10. Then identify the x-intercept.
Leona [35]
Graph the equation on a graph then the x intercept will be shown, the x intercept is -2.
3 0
3 years ago
Read 2 more answers
Help asap plsss ----------------------
d1i1m1o1n [39]

Answer:

g(x) = |x-7|+4

Step-by-step explanation:

If we imagine trying to find the vertex of f(x) or the lowest part, we can always input x and y into each equation and see if they equal on either side.

The vertex is at points (7,4)

4=|7-7|+4 : 4=4.

4 0
3 years ago
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