The value of 5x2 - 11x + 18 is when x = 2.4 and whenx = -3.
2 answers:
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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!
Answer:
It is Milk
Step-by-step explanation:
The liquid in the bottle has mass given in grams and the mass of that substance is 117 grams.
The volume of the substance is 15 cubic centimeters.
Now, using the formula of density we can estimate which substance could it be.
, where 'd', is the density, 'm' is the mass, and 'v' is the volume of the substance.
Plugging the value of mass and volume we get:
So the density of the substance is 7.8 grams per cubic centimeter.
It cannot be water since the density of water is 1 grams per cubic centimeter.
It cannot be gasoline because its density is 0.77 grams per cubic centimeter.
It cannot be mercury because the density of mercury is 13.56 grams per cubic centimeter.
Since, the density in this case matches the density of thick milk and hence,therefore, the liquid in the bottle is milk.