The F-test is used in regression analysis to test the hypothesis that all model parameters are zero. It is also used in statistical analysis when comparing statistical models.
Statistical models that have been fitted using the same underlying factors and data set to determine the model with the best fit. That is:
H₀ : B₁ = B₂ = ............. = Bₓ =0
H₁: Bₙ ≠ 0 for at least one j.
The F-test was developed by Ronald A. Fisher (hence F-test) and is a measure of the ratio of variances. The F-statistic is defined as:
F = [tex]\frac{explained variables}{unexplained variables}[/tex]
A general rule of thumb that is often used in regression analysis is that if
F > 2.5then we can reject the null hypothesis. We would conclude that there is a least one parameter value that is nonzero.
The F-distribution is generally a skewed distribution and also related to a chi-squared distribution. The f distribution is the ratio of X1 random chi-square variable with degrees of freedom ϑ1 and X2 random chi-square variable with degrees of freedom ϑ2. (In other words each of the chi-square random variable has been divided by its degrees of freedom)
The F-distribution is generally a skewed distribution and also related to a chi-squared distribution. The f distribution is the ratio of X1 random chi-square variable with degrees of freedom ϑ1 and X2 random chi-square variable with degrees of freedom ϑ2. (In other words each of the chi-square random variable has been divided by its degrees of freedom)
F =[tex]\frac{x_{1}/v_{1} }{x_{2}/v_{2} }[/tex]
Learn more about F-distribution:
https://brainly.com/question/26770623
#SPJ4
i,d like to order 7 halves for my family plus i want some extra for y 6 friends they'll each want a quarter whats the answer
The total number of cupcakes ordered, using proportions, is of:
5.
What is a proportion?A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem to find the desired amounts in the same context of the problem.
These amounts are found using basic arithmetic operations, especially multiplication and division, with the unit rates in the context of the problem.
In this problem, the amounts are given as follows:
Family: Seven halves of cupcakes = 7/2 = 3.5 cupcakes.Friends: Six quarters of cupcakes = 6/4 = 1.5 cupcakes.The total number of cupcakes that will be ordered is the sum of the amounts that will be needed for the family and for the friends, hence:
3.5 cupcakes + 1.5 cupcakes = 5 cupcakes.
Missing InformationThe problem is:
I'd like to order 7 halves of cupcakes for my family plus an amount for six friends, considering that each of them wants a quarter. What is the total amount?
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
an inverted cone has a height of 11 inches and an initial radius of 18 inches. the volume of the inverted cone is decreasing at a rate of 541 cubic inches per second, with the height being held constant. what is the rate of change of the radius, in inches per second, when the radius is 5 inches?
Answer:
-4.697 in/s
Step-by-step explanation:
You want to know the rate of change of radius of a cone 11 inches high with a radius of 5 inches and a volume that is decreasing at the rate of 541 cubic inches per second.
VolumeThe volume of a cone is given by ...
V = π/3r²h
The rate of change is found by implicit differentiation:
V' = (π/3)((2rr')h +r²h')
Here, the height is constant, so h' = 0. Solving for r', we find ...
r' = 3V'/(2πrh)
ApplicationUsing the given values of V', r, and h, we find the rate of change of radius to be ...
r' = 3(-541 in³/s)/(2π(5 in)(11 in)) = -1623/(110π) in/s ≈ -4.69652 in/s
The radius is decreasing at about -4.697 inches per second.
__
Additional comment
The initial radius of the cone is irrelevant to the problem, since we want to know the rate of change at a specific different radius. Whether the cone is inverted or not is also irrelevant to its volume.
Write an equation in standard form with an x-intercept of 4 and a y-intercept of 5.
Equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.
Given:
x - intercept = 4
y - intercept = 5
At x intercept y = 0 and at y intercept x = 0
(4,0) and (0,5)
slope = 5-0/0-4
= 5/-4
m = -5/4
substitute (4,0) and m value,
y = mx+c
0 = -5/4*4 +c
0 = -5 + c
c = 5
y = mx + c
y = -5/4(x) + 5.
Therefore equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.
Learn more about the equation here:
https://brainly.com/question/10413253
#SPJ1
write an equation of the line in slope intercept form
The equation of the line in slope intercept form is y = (-4/3)x .
In the question ,
a line graph is given ,
we need to find the equation of that line .
the two points that are given on the line graph are (-3 , 4) and (0 , 0) ,
the equation of the line passing from the points (x₁ , y₁) with slope m in the slope intercept form is given by
(y - y₁) = m(x - x₁) .
we first need to find the slope .
So , m = (0 - 4)/(0 + 3)
m = -4/3
The equation of the line passing from the points (-3 , 4) with slope -4/3 , in the slope intercept form is
(y - 4) = (-4/3)(x -(-3))
y - 4 = (-4/3)(x + 3)
y - 4 = (-4/3)x - 4
y = (-4/3)x - 4 + 4
y = (-4/3)x
Therefore , The equation of the line in slope intercept form is y = (-4/3)x .
Learn more about Equation Of Line here
https://brainly.com/question/21298390
#SPJ1
a man 6 ft tall walks at the rate of 5 ftsec toward a streetlight that is 16 ft above the ground. at what rate is the length of his shadow changing when he is 10 ft from the base of the light?
The rate at which length of shadow of person changing is 3 ft /sec.
What is meant by time rate?The literal formula for the relationship between distance, rate, and time is distance=rate×time=rtH = Height of streetlight; 16 ft
h = Height of man; 6 ft
x = Length of man's shadow.
s = Distance from streetlight to man.
Using the similarities of the triangles.
H/h = (s + x)/x
Hx = h(s + x)
Differentiate with respect to 't' on both sides.
H(dx/dt) = h(ds/dt + dx/dt)
Put the values.
16(dx/dt) = 6(5 + dx/dt)
16(dx/dt) = 30 + 5dx/dt
10dx/dt = 30
dx/dt = 3 ft /sec
Thus, the rate at which length of shadow of person changing is 3 ft /sec.
To know more about the time rate, here
https://brainly.com/question/119866
#SPJ4
solve for the variable in 7/26=25/x
Answer:
x = 650/7
Step-by-step explanation:
7/26 = 25/x
7*x = 25*26
7x = 650
x = 650/7
Check:
7/26 = 25/(650/7)
7/26 = 25*7/650
7/26 = 175/65
7*650 = 26*175 = 4550
please help me out on this ASAP!!
The value of k for which the quadratic equation 4s² - 4s + (k - 2) has one real solution is:
k = 16.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by the rule presented as follows:
y = ax² + bx + c
The discriminant of the quadratic function is given as follows:
Δ = b² - 4ac.
The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:
Δ > 0: two real solutions.Δ = 0: one real solution.Δ < 0: two complex solutions.In this problem, the equation is given as follows:
4x² - 4s + (k - 2) = 0.
Hence the coefficients are given as follows:
a = 4, b = -4, c = k - 2.
Hence the discriminant is:
Δ = (-4)² - 4(4)(k - 2)
Δ = 16 - 16k + 32
Δ = 48 - 3k
It has one real solution if Δ = 0, hence:
48 - 3k = 0
3k = 48
k = 48/3
k = 16.
More can be learned about the discriminant of quadratic equation at https://brainly.com/question/17097611
#SPJ1
Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.
Answer:
For part a you would decompose the fraction into two independent fractions with the following form:
() = ()/( x^2+5)(x ^2+3x−4) = (Ax + B)/(x^2+5) + (Cx + D)/(x ^2+3x−4)
Combining these fractions we get:
((Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5))/( x^2+5)(x ^2+3x−4) = ()/( x^2+5)(x ^2+3x−4)
Thus we can say: (Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5) = ()
You then simplify the equation on the left by combining like terms and solve the system of equations that arise corresponding with ().
You would follow a similar process for part b as well.
Step-by-step explanation:
state: how heavy a load (in pounds) is needed to pull apart pieces of douglas fir 4 inches long and 1.5 inches square? data from students doing a laboratory exercise are given.
The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).
Define confidence interval.In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. The size of a 90% confidence interval for a given estimate is one way to gauge how "excellent" it is; the greater the interval, the more care must be used when utilizing the estimate. Confidence intervals serve as a crucial reminder of the estimates' limits.
Given,
Data set: (33190, 31860, 32590, 26520, 33280, 32320, 33020, 32030, 30460, 32700, 23040, 30930, 32720, 33650, 32340, 24050, 30170, 28730, 31920)
The normal distribution's standard deviation, s = 3000 pounds
95% confidence interval
N = 20 observations were made.
Mean = 30,800
Margin of error :
z₇ × √3000².20
±1.314.8079
Confidence interval
= Mean + Margin of error
= 30,800 ±1.314.8079
= 29,485.192 , 32,114.8
The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).
To learn more about confidence interval, visit:
https://brainly.com/question/13077081
#SPJ4
What integers are the solutions to
|x-4| < 8 and |-3x| > 12
Answer:
x-4<12 x<-4
-3x<12
-3x/-3=x
12/-3=-4
x-4+4=x
8+4=12
Hey, guys! How is your day? (°ω°)
Wilson paints 40% of a bookcase in 20 minutes.
Write an equation using equal fractions to represent this situation. Use a box to represent the time it takes to paint the whole bookcase.
The time it takes to paint the whole bookcase is 50 minutes.
How to calculate the value?From the information, Wilson paints 40% of a bookcase in 20 minutes.
Let the time taken to paint the whole bookcase be x. This will be illustrated as:
20/x = 40/100
Cross multiply
40x = 100 × 20
40x = 2000.
Divide
x = 2000 / 40
x = 50
The time taken is 50 minutes.
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
Work out the 3rd term.
in the
geometric sequence
generated by 5n
The third term in the sequence generated by 5n is 15.
According to the question,
We have the following information:
The sequence is given by the formula 5n.
In this case, n represents the number of the term.
(Note that the sequence generated by this formula can not be a geometric sequence because the common ratio of these terms is not the same.)
So, we have to find the 3rd term of this sequence. Then, we will find the value of this sequence by putting the value of n as 3.
So, we have the following expression:
5*3
15
Hence, the third term in the sequence generated by 5n is 15.
To know more about term in the sequence here
https://brainly.com/question/26949253
#SPJ9
I need help I don’t understand how it’s wrong
==========================================
Explanation:
If it is possible to draw a single vertical line through more than one point on the blue graph, then that graph is not a function. We consider it failing the vertical line test. Such a thing happens in the middle of the top row (graph 2). A vertical line intersects the sideways parabola at more than one point.
Recall a function is when any given input leads to exactly one output. We can't have the input x = 4 lead to both y = 1 and y = -3 at the same time for instance.
Graph 4 is another instance where we don't have a function for similar reasoning. This graph fails the vertical line test. So does graph 6.
The other graphs (1, 3, and 5) all pass the vertical line test since it's not possible to draw a single vertical line to intersect through more than one blue point.
please help look at picture
PLEASE HELP ME EASY 8TH GRADE MATH!!!!
Answer: The probability is 3 out of 20
Step-by-step explanation:
what kind of autocorrelation is assumed in the classical linear regression model? what kind of autocorrelation is assumed in the classical linear regression model? positive autocorrelation negative autocorrelation no autocorrelation serial correlation g
We use the Serial Autocorrelation in the classical linear regression model.
In the classical linear regression model the serial autocorrelation is assumed to solve the problem.
Hence, we use the Serial Autocorrelation in the classical linear regression model.
Learn more about Linear Regression here https://brainly.com/question/25987747
#SPJ4
help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the slope of the line that passes through the points (-6, -6) and (-9, -5)? Write your answer in the simplest form.
Answer: -1/3
Step-by-step explanation:
The formula for slope =y1-y2/x1-x2. You first subtract the numbers for the y coordinate which is -6-(-5), and thats -1. Then you subtract the x coordinates. -6-(-9)=3. So the slope is -1/3
T2 Midterm Re
1. X and Y are two fractions. X is greater than 0 but less than 1.
Which statement describes the product of X and Y?
A.
The product is less than -1.
B. The product is greater than -1 but less than 0.
C. The product is greater than 0 but less than 1.
D. The product is greater than 1.
Answer: The correct answer is C. The product is greater than 0 but less than 1.
Step-by-step explanation:
X and Y are both fractions
X is greater than 0 but less than 1
X * Y > 0 and < 1
The product of these two fractions will result in a fraction between 0 and 1.
For example:
1/2 x 1/2 =1/4, 1/6 x 2/6 = 1/18, 1/10 x 5/6 = 1/12
SOLVE FOR X answer .
Answer:
31
Step-by-step explanation:
x+10+2x+20+2x-5=180
5x+25=180
5x=155
x=31
evaluate the expression 2x^3 - 14 when x=2
Answer:
-2
Step-by-step explanation:
2(2)*3-14
4*3-14
12-14
-2
Please help thank you
By comparing the fractions of rocks that skip over the poind for Jessica and Henry, we will see that Jessica gets more rocks to skip over the pond.
Who gets more rocks to skip over the pond?We know that for every 9 rocks that Herny throws, 5 skip over the pond. Then the fraction for Henry is:
H = 5/9
While for Jessica we know that for every 12 that she throws, 7 skip over the pond, so her fraction is:
J = 7/12
Now we only need to see which one of the fractions is larger.
If we simplify both we will get:
H = 5/9 = 0.556
J = 7/12 = 0.583
So we can see that Jessica's fraction is larger, which means that she will get more rocks.
Learn more about fractions:
https://brainly.com/question/11562149
#SPJ1
a catering company needs 8.75 lb of shrimp for a small party. they buy lb of jumbo shrimp,3 2 3 lb of medium-sized shrimp, and some mini-shrimp. how many pounds of mini-shrimp do they2 5 8 buy?
Finally, we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.
Given that;
A catering company needs 8.75 lbs of shrimp for a small party. they buy [tex]3\frac{2}{3}[/tex] lbs of jumbo shrimps, [tex]2\frac{5}{8}[/tex] lbs of medium-sized shrimps, and some mini-shrimps.
The total of 8.75th is changed as [tex]8\frac{3}{4}th\\[/tex]
Sum of [tex]3\frac{2}{3}[/tex] + [tex]2\frac{5}{8}[/tex] this is bought by the company.
So, to purchase the remaining [tex]8\frac{3}{4}th\\[/tex] - [tex]3\frac{2}{3}[/tex] - [tex]2\frac{5}{8}[/tex]
We use a common denominator of 24 for the fraction parts.
Change [tex]8\frac{3}{4}[/tex] as [tex]8\frac{18}{24}[/tex]
Similarly, convert;
[tex]3\frac{2}{3}[/tex] as [tex]3\frac{16}{24}[/tex]
[tex]2\frac{5}{8}[/tex] as [tex]2\frac{15}{24}[/tex]
By solving all the above conversions, we get;
[tex]\frac{42-16-15}{24}[/tex] = 11/24
Considering all the factors together we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.
To learn more about denominator click here:
brainly.com/question/7067665
#SPJ4
An element with a mass of 420 grams decays by 7.5% per minute. To the
nearest minute, how long will it be until there are 210 grams of the element
remaining?
Answer: x= 9
Step-by-step explanation:
I just checked that its right!
Answer:
The correct answer would be 9
Step-by-step explanation:
Find the least common multiple of the given algebraic terms. x², 2xy, 3y
Step-by-step explanation:
common factor= x and y
remaining factor = x , 2 , 3
L.C.M = 6 x sq. y
Solve the inequality. x² + 4x - 21 ≥ 0
and please explain
Step-by-step explanation:
if the solution has "nice" numbers, we can split the expression into 2 factors in the form
(x + a)(x + b) = x² + (a+b)x + ab
as this is equal to x² + 4x - 21.
ab = -21
so, one is positive and one is negative.
and 4 = a + b
we know the typical factors of 21 : 3×7
and then we see easily : 7-3 = 4
so,
we have
(x + 7)(x - 3) >= 0
this has 2 x-intercepts (x-values when y = 0) :
x = -7
x = 3
because the coefficient of x² is positive (1), we know that the parabola (or quadratic equation) is opening upwards.
that means the y-values for x-values between -7 and +3 are negative (< 0), but the y-values for everything else are positive.
so, the solution are the intervals
x <= -7 and x >= 3
in these areas is the expression x² + 4x - 21 >= 0.
Solve the equation given a domain of {-3}.
3x - 2y = 5
Solution of the equation 3x-2y = 5 for domain {-3} is (-3,-7).
Given,
Eq => 3x - 2y = 5
Domain = x = -3
Put x = -3 in equation
3(-3) - 2y = 5
-9 - 2y = 5
-9 - 5 = 2y
-14 = 2y
y = - 14 / 2
= -7
Hence, solution is (-3,-7).
To learn more about Solution here:
https://brainly.com/question/1616939
#SPJ1
What is the domain of the following function
The domain of the given function is equal to: {-4, 2, 6, 9}.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values or numbers to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
Generally speaking, the horizontal extent of the graph of a function represents all domain values and they are read and written from the smallest to the largest numerical values, and from the left of a graph to the right.
By critically observing the given function, we can reasonably and logically deduce the following:
Domain = {-4, 2, 6, 9}.
Range = (-3, 1).
Read more on domain here: brainly.com/question/17003159
#SPJ1
A group of 4 people go to a restaurant and the bill without tax comes to $105.73. Tax is 6%. Remember to round to the nearest hundredth because this is money. After tax is added, you want to leave a 20% tip on the new total. The group of 4 people decides to split the total cost equally. How much will each person pay?
The amount of money paid by each of the 4 persons will be $33.6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a group of 4 people go to a restaurant and the bill without tax comes to $105.73. The tax is 6%. Remember to round to the nearest hundredth because this is money. After-tax is added, you want to leave a 20% tip on the new total.
Total cost = $105.73 x 1.06 x 120
Total cost = $134.48
Amount for each person,
A = $134.48 / 4
Amount = $33.62
Therefore, the amount of money paid by each of the 4 persons will be $33.6.
To know more about an expression follow
https://brainly.com/question/3044443
#SPJ1
I need to find the equation for y=
For the format f(x)=|x|.
Answer:
[tex]f(x)=-|2x|[/tex]
Step-by-step explanation:
First, find the slope of the right side of the graph. It is -2. But because an absolute value always makes the value inside positive, we put the negative sign outside the absolute value.
The rule of thumb for absolute value graphs is: if it opens upwards, the absolute value is positive; if it opens downwards, the absolute value is negative.
So, the equation we can construct from this information is:
[tex]f(x)=-|2x|[/tex]