Answer:
Step-by-step explanation:
The slope-intercept form of the line is:
Where m is the slope and b the intersection with the y-axis.
You can see in the graph that line intersect the y-axis at , then:
Choose two points and substitute them into the formula for calculate the slope. This is:
Let's pick the points (-4,4) and (-6,8). The the slope is:
Substituting into the equation, you get:
So firstly, I'm going to be converting the mixed number into an improper fraction. To do this, multiply the whole number by the denominator and then add that product with the numerator and that will be your new numerator. In this case:
3 × 8 = 24, 24 + 3 = 27.
Now since they have the same denominator, you can subtract the numerators.
Now simplify the number as such:
<u>In short, your answer is -17/4, or -4 1/4.</u>
Answer:
The answer is 13.6
Step-by-step explanation:
13.6 in fraction form is or
Answer:
b0= 144.59
b= -2.12
Se²= 1.02
99%CI E(Y/X=35): [68.78; 71.99]
Step-by-step explanation:
Hello!
I've arranged the given data:
X: 37.0, 36.4, 35.8, 34.3, 33.7, 32.1, 31.5
Y: 65.0, 67.2, 70.3, 71.9, 73.8, 75.7, 77.9
The equation of the linear regression model is:
Yi= β₀ + βXi + εi
Where
Yi is the dependent variable
Xi is the independent variable
εi represents the errors or residues
β₀ is the intercept of the line
β is the slope
The conditions to make a linear regression analysis are:
For each given value of X, there is a population of Y~N(μy;σy²)
Each value of Y is independent of the others.
The population variances of each population of Y are equal.
From these conditions the following characteristic is deduced:
εi~N(0;σ²)
The parameters of the regression are:
β₀, β, and σ²
If the conditions are met then you can estimate the regression line:
Yi= bo * bXi + ei.
And the point estimation of the parameters can be calculated using the formulas:
β₀ ⇒ b0= (∑y/n)-b(∑x/n)
β ⇒ b= [∑xy- ((∑x)(∑y))/n]/(∑x²-((∑x)²/n))
σ²⇒ Se²= 1/(n-2)*[∑y²-(∑y)²/n - b²(∑x²-(∑x)²/n)]
n= 7
∑y= 501.80
∑y²= 36097.88
∑x= 240.80
∑x²= 8310.44
∑xy= 17204.87
b0= 144.59
b= -2.12
Se²= 1.02
The estimated regression line is:
Yi= 144.59 -2.12Xi
You need to calculate a 99%CI E(Y/X=35), the formula is:
(b0 + bX0) ± *
(144.59 + (-2.12*35)) ± 4.032*
[68.78; 71.99]
With a 99% confidence level youd expect that the interval [68.78; 71.99] contains the true value of the average of Y when X= 35.
I hope it helps!