Professor Isaac Asimov was one of the most prolific writers of all time. Prior to his death, he wrote nearly 500 books during a 40-year career. In fact, as his career progressed, he became even more productive in terms of the number of books written within a given period of time. The data given in increments of 100:
Number of books, x: 100 200 300 400 500
Time in months, y: 237 350 419 465 507
a. Assume that the number of books x and the time in months y are linearly related. Find the least-squares line relating y to x.
b. Plot the time as a function of the number of books written using a scatterplot, and graph the least-squares line on the same paper. Does this seem to provide a good fit to the data points?
c. Construct the ANOVA table for the linear regression.
Answers
Answer:
Step-by-step explanation:
n = sample size = 5
a) Let us determine the sum
[tex]\sum x_i= 100+200+300+400+490=1490[/tex]
[tex]\sum x_i^2= 100^2+200^2+300^2+400^2+490^2=540100[/tex]
[tex]\sum y_i = 237+350+419+465+507=1978[/tex]
[tex]\sum y_i^2= 237^2+350^2+419^2+465^2+507^2=827504[/tex]
[tex]\sum x_i y_i=100 \times 237 + 200\times350+300 \times 419 + 400 \times 465 + 490 \times 507=653830[/tex]
Now we can determine [tex]S_x_x, S_x_y, S_y_y[/tex]
[tex]S_x_x = \sum x_i^2-\frac{(\sum x_1)^2}{n} \\= 540100 - \frac{1490^2}{5} \\= 96080[/tex]
[tex]S_x_y = \sum x_i y_i -\frac{(\sum x_i)(\sum y_i) }{n} \\\\[/tex]
[tex]653830 - \frac{1490 \times 1978 }{5} = 64386[/tex]
[tex]S_y_y = \sum y_i^2-\frac{(\sum y_i)^2 }{n} = 82750-\frac{1978^2}{5} \\\\= 45007.2[/tex]
The estimate b of the slope β is the ratio of [tex]S_x_y[/tex] and [tex]S_x_x[/tex]
[tex]b = \frac{S_x_y}{S_x_x}[/tex]
[tex]\frac{64386}{96080} = 0.67[/tex]
The mean is the sum of all value divide by number of values
[tex]\bar x= \frac{\sum x_i}{n} \\\\= \frac{100+200+300+400+490}{5} \\\\= \frac{1490}{5} = 298[/tex]
[tex]\bar y= \frac{\sum y_i}{n} \\\\= \frac{237+350+419+465+507}{5} \\\\= \frac{1978}{5} = 395.6[/tex]
The estimate a of the intercept is
[tex]a = \bar y - b \bar x[/tex]
[tex]= 395.6 - 0.69 \times 298\\= 195.9[/tex]
General least square equation;
[tex]\bar y = \alpha + \beta x[/tex]
replace alpha by a = 3 and beta by b = 0.67 in general least equation
y = a + bx
195.9 + 0.67x
b)
Scatter plot is shown in the attached file
x is on the horizontal axis
y is n the vertical axis
The degree of freedom of regression is 1
because we use one variable s predictor variable
[tex]d_f_R = 1[/tex]
The degree of freedom of error is the sample size n decrease by 2
[tex]d_f_E =n-2= 5 - 2=3[/tex]
Total df is equal to the sum of seperate degree of freedom dfR and dfE
total df = 1 +3 4
[tex]SSR = \frac{(S_x_y)^2}{S_x_x} = \frac{64386^2}{96080} \\\\= 43146.9296[/tex]
Total SS =Syy= 45007.2
SSE + Total SS = SSR
= 45007.2 - 43146.9296
= 1860.2705
Related Questions
Gymnastics lessons cost $10 per session, plus a one-time fee of $25. Shawn went to 7 sessions. Write an equation that can be used to find how much Shawn paid ?
Answers
Answer: y=10x+25
y=10(7)+25
=70+25
=$95
Step-by-step explanation:
What’s the correct answer for this?
Answers
Answer:
A.
Step-by-step explanation:
tan x= 6/8
usually tan θ = perpendicular / base
So,
we get perpendicular = 6, base = 8
Now using Pythagorean Theorem to find hypotenuse
hyp² = base² + Perp²
hyp² = 8² + 6²
hyp²= 64 + 36
hyp²=100
Taking sq root on both sides
hypotenuse = 10
Now
sin θ = Perpendicular / Hyp
sin x = 6 / 10
Now
cos θ = base / Hyp
cos x = 8 / 10
What is the vertex of the graph of the function f(x) = x2 + 8x - 2 ?
(-4, 18)
(0, -2)
(-8, -2)
(-4, -18)
Answers
Answer: (-4,-18)
Step-by-step explanation: If you use desmos you can graph the equation to find the vertex.
The vertex of the graph of function f(x) = x² + 8x - 2 is (-4, -18)
What is the vertex of the graph of a quadratic function?In a quadratic function, the vertex of the graph refers to the highest or lowest possible outcome of the function. In a graph, the vertex is the highest or lowest point on the parabola,
Given that:
f(x) = x² + 8x - 2
where;
a = 1b = 8c = - 2By using the vertex formula to find the x-value;
[tex]\mathbf{x = \dfrac{-b}{2a}}[/tex]
[tex]\mathbf{x = \dfrac{-8}{2(1)}}[/tex]
x = -4
So,
y = (-4)² + 8(-4) - 2
y = 16 -32 -2
y = -18
Therefore, the vertex of the graph of function f(x) = x² + 8x - 2 is (-4, -18)
Learn more about the vertex of the graph function here:
https://brainly.com/question/1305555
#SPJ2
Find the solution to the system of equations.
−2x+2y=−4
3x+3y=−18
Answers
Answer:
Step-by-step explanation:
-6x + 6y = -12
6x + 6y = -36
12y = -48
y = -4
3x - 12 = -18
3x = -6
x = -2
(-2, -4)
Sara needs 3 cups of orange juice and 2 cups of pineapple for punch recipe. She only has a half cup measure. How many half cups of juice does she need?
Explain your thinking here:
write your answer here:
Answers
Answer:
10
Step-by-step explanation:
3+2 = 5
5x2 (Because only half cups)
= 10
There are 12 inches in 1 foot. Write 75 inches in feet and inches
Answers
7 feet and 9 inches
Answer:6.25
Step-by-step explanation:
What is the disciminant of 3x^2-10x=-2
Answers
Answer:
76
Step-by-step explanation:
First get the equation into the form
ax^2 +bx+c =0
3x^2-10x+2=-2+2
3x^2-10x+2 =0
The discriminant is
b^2 -4ac where a=3 b = -10 c =2
(-10)^2 - 4(3)(2)
100 - 24
76
PLS HELP ASAP !!!! Giving brainlist!
Answers
First one (on the left) is 2) associative property because we are regrouping terms or re-associating them based on the parenthesis. Think of the parenthesis like a tent or a house that separates off the stuff outside. First 27 and 36 are grouped, then we move the parenthesis so that 52 and 27 are grouped now.
Second one (on the right) is 1) commutative. The commutative multiplication property says we can multiply two numbers in any order. For example, 4*9 = 36 and 9*4 = 36. The 4 and 9 swap places. In this problem, the 3 and 4x swap places. The use of parenthesis isn't necessary, though it is sometimes used to imply multiplication.
Answer:
1) Associative property
2) Commutative property
The hypotenuse of a 30°-60°-90° triangle measures 10 inches. Which could be the length of a leg of the triangle?
Answers
Answer:
6 and 8
Step-by-step explanation:
The hypotenuse of a 30°-60°-90° triangle measures 10 inches.
To find the length of one of the legs, we use the idea of Pythagorean Triples.
Pythagorean Triples are any set of three numbers that satisfies the Pythagorean Theorem. Some common examples are:
3, 4 and 55, 12 and 139, 40 and 41Note that in a Pythagorean Triple,
The longest length is always the Hypotenuse.New Triples can be formed from product of existing triples.In our given triangle, the Hypotenuse=10 Inches
Consider the Pythagorean Triple 3,4, and 5
5 is the HypotenuseMultiply the Triples by 2, we obtain:6, 8 and 10 (in which 10 is the hypotenuse)Therefore, 6 and 8 could be the length of a leg of the 30°-60°-90° triangle.
4 ÷ 1/5 = 20 because
Answers
Step-by-step explanation:
BECAUUUUSE ;
[tex]4 \div \frac{1}{5} = 20 \\ \frac{4}{1} \div \frac{1}{5} = 20 \\ \frac{4}{1} \times \frac{5}{1} = 20 \\ \frac{20}{1} = 20[/tex]
Answer:Because the divide sign change to multiplication sign, and when this happens denominator in the right hand side will become numerator,while the formal numerator will become denominator.
Step-by-step explanation:
4 ➗ 1/5
4 x 5/1=20
I really just need a simple STEP-BY-STEP explanation on how you do percentages.
Answers
Someone please help me with math. Thank You
Answers
Answer:
4) 64 cubic inches
Step-by-step explanation:
8x8 = 64
Starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a
horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to
right. Write a cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in
inches) as a function of time t (in seconds)
a=
Answers
Answer:
Step-by-step explanation:
amplitude of oscillation a = 12 / 2 = 6 inches.
time period T = 2 s
b = angular frequency = 2π / T
= 2π / 2
= π
so putting the values in the equation
d = a cos ( b t )
d = 6 cos ( π t )
Answer:
there are two more questions and the answers are 0.5 is the least positive amount of the pendulum and 4.243=y when x=4.25
Step-by-step explanation:
The length of a rectangle is seven less than twice the length of its width. If the area of the rectangle is 15 square meters, find the value of x.
Answers
Answer:
Length is 3 meters and the Width is 5 meters
Step-by-step explanation:
L*W=15
L=2W-7
(2W-7)W=15
[tex]2W^{2} -7W=15\\2W^{2} -7W-15=0[/tex]
(2W+3)(W-5)=0, don't use (2W+3)=0, because it gives you a negative dimension.
W=5, L=3
Hannah is setting up chairs for the class play. The room has 20 chairs. What are the different ways she can arrange the chairs in a rectangle?
Answers
Answer:
Have them 4 by 5.
Step-by-step explanation:
If you she but 5 chairs in a row, then 3 on the side of the chairs. That would create a backward "L" type of shape.
For example, (The "o" is a chair)
OOOOO
O
O
O
As you see the the top are the 5 chairs, then side are are the 4 chairs.
Then, you will do the exact same thing but on the opposite side.
Here is the next example.
OOOOOO
O O
O O
O O
OOOOOO
Basically, arranging the chairs 4x5, it would make a rectangle.
100 POINTS
PLEASE PROVIDE STEPS.
THANK YOU!!!
Answers
Answer:
2/π
h(x) is concave up on the intervals (-∞, -1/√3) and (1/√3, ∞).
h(x) is concave down on the interval (-1/√3, 1/√3).
Step-by-step explanation:
f(x) = sin x
The average value of a function between x=a and x=b is:
avg = 1/(b−a) ∫ₐᵇ f(x) dx
avg = 1/(π−0) ∫₀ᵖⁱ sin x dx
avg = 1/π (-cos x) |₀ᵖⁱ
avg = 1/π (-cos π − (-cos 0))
avg = 1/π (1 + 1)
avg = 2/π
h(x) = x⁴/12 − x²/6
Find the second derivative.
h'(x) = x³/3 − x/3
h"(x) = x² − ⅓
Factor using difference of squares.
h"(x) = (x − 1/√3) (x + 1/√3)
h"(x) = 0 when x = ±1/√3. Evaluate the sign of h"(x) in each interval.
-∞ < x < -1/√3, h"(x) > 0.
-1/√3 < x < 1/√3, h"(x) < 0.
1/√3 < x < ∞, h"(x) > 0.
h(x) is concave up on the intervals (-∞, -1/√3) and (1/√3, ∞).
h(x) is concave down on the interval (-1/√3, 1/√3).
Answer:
2/π
h(x) is concave up on the intervals (-∞, -1/√3) and (1/√3, ∞).
h(x) is concave down on the interval (-1/√3, 1/√3).
Step-by-step explanation:
A researcher conducts an independent-measures study examining the effectiveness of a group exercise program at an assisted living facility for elderly adults. One group of residents is selected to participate in the program, and a second group serves as a control. After 6 weeks, the researcher records a combined score measuring balance and strength for each individual. The data are as follows:
Control Exercise n = 10 n = 15 M = 12 M = 15.5 SS = 120.5 SS = 190.0
a. Does the exercise program have a significant effect? Use an alpha level of .05, two tails.
b. Compute Cohen�s d to measure the size of the treatment effect.
Answers
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images below to see the step by step explanation to the question above.
What’s the correct answer for this? Select the ones that apply
Answers
Answer:
A: -2
B: -10
Step-by-step explanation:
A: the slope of line b is -2
B: Point: (-6,2)
So x= -6 and y = 2
Putting in slope intercept formula for finding b
y=mx+b
2=(-2)(-6)+b
2= 12 + b
b = 2-12
b= -10
The y-intercept of line b is -10
Graph the solution set for each given inequality
a. x > 7.75
b. x Underscore-< 5/2
I just want to see how to graph it. Sorry if that's too much to ask :P
Answers
Answer:
see the attachments
Step-by-step explanation:
An inequality without the "or equal to" case is graphed with an open circle at its boundary point. If the "or equal to" case is included, then the dot at the boundary is filled in (a solid dot). The number line is shaded to the left or right of the boundary point, depending on whether the set being graphed includes values less than or greater than the boundary value. Usually, a line extending indefinitely will have an arrow on its end. (Not here, because the program used doesn't easily support drawing arrows.)
__
a. The boundary point at x=7.75 has an open circle, and the shading of the number line extends indefinitely to the right from there.
__
b. The boundary point at x=2.5 is a solid dot, and the shading extends indefinitely to the left.
Plz help me find the area of this polygon
Answers
Answer:
It is 4
Step-by-step explanation: To find the area you multiply the numbers.
What is true when you rent? A.you build equity in your house,B.you are responsible for any repairs,c. You pay fewer up front costs
Answers
Answer: C you pay fee fewer upfront cost
Step-by-step explanation:
If 2 pounds of steak can serve 5 people how many pounds will serve 13 people
Answers
Step-by-step explanation:
wait sorry that was wrong
Answer:
5.2
Step-by-step explanation:
The answer is 5.2 pounds of meat. To find this just divide the number of people by what the information you have about servings. 13/5=2.6(number of sets), then you multiply that by how many pounds are in each set.
∫ ( cos^4(3x)) d x
Answers
Answer:
⅜ x + ¹/₁₂ sin(6x) + ¹/₉₆ sin(12x) + C
Step-by-step explanation:
∫ cos⁴(3x) dx
Use power reduction formula:
⅛ ∫ (3 + 4cos(6x) + cos(12x)) dx
⅜ ∫ dx + ½ ∫ cos(6x) dx + ⅛ ∫ cos(12x) dx
⅜ ∫ dx + ¹/₁₂ ∫ 6 cos(6x) dx + ¹/₉₆ ∫ 12 cos(12x) dx
⅜ x + ¹/₁₂ sin(6x) + ¹/₉₆ sin(12x) + C
if you had a sale price of $40 and the percent of your discounts 25% what was the original price.
Answers
Answer:
$ 50
Step-by-step explanation:
Original price = Sale price + discount
= 40 + 25% of 40
= 40 + 0.25 * 40
= 40 + 10
Original price = $50
The article "Snow Cover and Temperature Relationships in North America and Eurasia"† used statistical techniques to relate the amount of snow cover on each continent to average continental temperature. Data presented there included the following ten observations on October snow cover for Eurasia during the years 1970-1979 (in million km2): 6.5 12.0 14.9 10.0 10.7 7.9 21.9 12.5 14.5 9.2 What would you report as a representative, or typical, value of October snow cover for this period, and what prompted your choice?
Answers
Answer:
Step-by-step explanation:
From the given information,
The ten observation data on october snow cover for Eurasia during the years is 6.5, 12.0, 14.9, 10.0, 10.7, 7.9, 21.9, 12.5, 14.5, 9.2
What would you report as a representative, or typical, value of October snow cover for this period, and what prompted your choice?
For the given data, 21.9 is an outlier, so trimmed mean would be good choice for the researcher,
Remove the smallest and the largest values to compute the trimmed mean
[tex]\bar x = \frac{12.0+14.9+10.0+10.7+7.9+12.5+14.5+9.2}{8} \\\\=\frac{91.7}{8} \\\\=11.465[/tex]
g(x) = 4x2 – 3x + 7
Find g(3)
Simplify your answer
Answers
Answer:
32
Step-by-step explanation:
g(x) = 4x² - 3x + 7
g(3) = 4(3)² - 3(3) + 7
g(3) = 4(9) - 9 + 7
g(3) = 36 - 9 + 7
g(3) = 25 + 7
g(3) = 32
Can someone help me please
Answers
Brainliest to whoever gets this CORRECT.
Answers
Answer:
yes
Step-by-step explanation:
yes
how do i solve 4/5 divided by 3/4
what is the answer please help
Answers
Answer:16/15 or 1 1/15
Step-by-step explanation:
4/5 ➗ 3/4
4/5 x 4/3
(4 x 4) ➗ (5 x 3)
16 ➗ 15=16/15 or 1 1/15
angle relationships with parallel lines
Answers
Answer: 136°
Step-by-step explanation:
In this angle relationship, it is a supplementary angles. because the parallel lines are separated by a line, the 2 angles make 180°.
180°=44°+x°
x=136°
