Temperature (x) 65 70 75 80 85 90 95 100 105
Number of ice cream cones sold per hour (y) 8 10 11 13 12 16 19 22 23
Note: Critical Value for n = 9 is 0.666

Calculate the linear correlation coefficient r, for temperature (x) and the number of ice cream cones sold per hour (y). (round to 3 decimal place)
Is there a linear relation between the two variables x, and y? Why? If yes, indicate if the relationship is positive or negative. (Hint: Compare the absolute value of r and critical value)
Construct the least-squares regression line for temperature (x) and the number of ice cream cones sold per hour (y) and interpret its slope. (round to 3 decimal place)
Predict the number of ice cream cones sold per hour when the temperature is 80 and calculate the residual for x = 80º. (round to nearest whole number)
Would it be reasonable to use the least-squares regression line to predict the number of ice cream cones sold when it is 50 degrees? Explain your answer.

Answers

Answer 1

Answer:

Step-by-step explanation:

Hello!

You have to calculate the linear correlation coefficient (r) between the variables

X₁: temperature

X₂: Number of ice cream cones sold per hour.

The formula to calculate the coefficient of linear correlation between the two variables is the following:

[tex]r= \frac{sumX_1X_2-\frac{(sumX_1)(sumX_2)}{n} }{\sqrt{[sumX_1^2-\frac{(sumX_1)^2}{n} ][sumX_2^2\frac{(sumX_2)^2}{n} ]} }[/tex]

∑X₁= 765; ∑X₁²= 66525 ∑X₂= 134 ∑X₂²= 2228 ∑X₁X₂= 11965 n=9

[tex]r= \frac{11965-\frac{765*134}{9} }{\sqrt{[66525-\frac{(765)^2}{9} ][2228-\frac{(134)^2}{9} ]} }[/tex]

r= 0.97

To test if there is a positive linear association between both variables the statistical hypotheses are:

H₀: ρ ≤ 0

H₁: ρ > 0

critical value 0.666

r= 0.97

The decision is to reject the null hypothesis, there is a positive linear correlation between the temperature and the number of ice cream cones sold per hour.

The regression line is

^Y= a + bX

where

a: represents the estimation of the y-intercept

b: represents the estimation of the slope

[tex]b= \frac{sumXY-\frac{sumXsumY}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]

b= 0.38

a= Y[bar]-bX[bar]

a= -17.69

The estimated regression line for the number of ice cream cones and the temperature is ^Y= -17.69 + 0.38Xi

To estimate the number of ice cream cones sold when the temperature is 80º you have to replace the value of X in the estimated regression line:

^Y= -17.69 + 0.38*80= 12.71

It is expected that they will sell 12.71 ≅ 13 ice cream cones when the temperature is 80º

You can use the estimation of the regression line to predict values within the range of definition of the independent variable, in this case from 65º to 105º of temperature, because it is within those values that you can be sure they have a linear association. Below or above you are not certain that their association is linear, it may be, for example exponential, or there may be no association between them.

Example: If the temperature is comfortable or cold, it is more likely that people won't buy ice creams, so for those values it will be no linear association  between them.

I hope this helps!


Related Questions

What does the constant 2.2 in L(D) represent?

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Answer:

The constant 2.2 in L(D) represent the brightness in lumens per square inch.

Step-by-step explanation:

What is the area of this parallelogram?
6 cm
2 cm

Answers

Answer:

12

Step-by-step explanation:

Area= base*height

Area= 6*2

Answer:

12cm

Step-by-step explanation:

hight & Base=6 cm & 2 cm

Formula for area: hight×base=6 cm×2 cm

12cm

Compute: 10:00 - 2:30

Answers

Answer:

4 hr and 30 minutes?

Step-by-step explanation:

You didnt really specify soo.    11    12    1   2   2:30

                                                 1hr   2hr  3hr 4hr  30 min

Answer:7:30

Step-by-step explanation:

where is the point (0, –4) located

Answers

4 points below the origin

Your teacher has 50 pencils. 9 of the pencils are green, 10 are yellow, 7 are
blue and the rest are red. Once a pencil is picked, assume it is not given
back to the teacher. What is the probability that the first 3 students pick a
yellow pencil, a blue pencil and a red pencil in that order? Is this a
dependent or independent event? *
A. Independent, 1/70
B. Dependent, 1/70
C. Independent, 41/3125
D. Dependent, 41/3125

Answers

Answer:

B. Dependent, 1/70

Step-by-step explanation:

The probability that the first pencil is yellow is 10/50.

There are now 49 pencils, so the probability that the second pencil is blue is 7/49.

There are now 48 pencils, so the probability that the third pencil is red is 24/48.

The total probability is (10/50) (7/49) (24/48) = 1/70.

Since the pencils aren't replaced after selection, each event changes the probability of the next, so the events are dependent.

A vendor at a street fair sells popcorn in cones, all of height 9 inches. The
sharing-size cone has 3 times the radius of the skinny-size cone. About how
many times more popcorn does the sharing cone hold than the skinny cone?

Answers

Answer:

The sharing cone holds about 9 times more popcorn than the skinny cone.

Step-by-step explanation:

The volume of a cone is given by the following formula:

[tex]V = \frac{\pi r^{2}h}{3}[/tex]

In which r is the radius and h is the height.

Two cones:

Both have the same height.

The sharing-size cone has 3 times the radius of the skinny-size cone.

Skinny:

radius r, height h. So

[tex]V_{sk} = \frac{\pi r^{2}h}{3}[/tex]

Sharing size:

radius 3r, height h. So

[tex]V_{sh} = \frac{\pi (3r)^{2}h}{3} = \frac{9\pi r^{2}h}{3} = 3\pi r^{2}h[/tex]

About how many times more popcorn does the sharing cone hold than the skinny cone?

[tex]r = \frac{V_{sh}}{V_{sk}} = \frac{3\pi r^{2}h}{\frac{\pi r^{2}h}{3}} = \frac{3*3\pi r^{2}h}{\pi r^{2}h} = 9[/tex]

The sharing cone holds about 9 times more popcorn than the skinny cone.

Write a recursive formula for the sequence

-1,-2,-3,-4...

Answers

Answer:

  f(1) = -1

  f(n) = f(n-1) -1

Step-by-step explanation:

The first term is -1. Each term is 1 less than the previous. These equations say that.

  f(1) = -1

  f(n) = f(n-1) -1

Ryan randomly draws equal sized cards labeled with letters A, B, C, D and F from a hat and records the results in the table. Find the theoretical and experimental probabilities of randomly drawing a card that is labeled with the letter C. Frequency A 36, B 50, C 111, D 59, F 44 total 300

Answers

Answer:

We have 5 cards, and if we assume that the probability of selecting a given card at random is the same for all the cards, then the probability of randomly drawing the card C out of the 5 cards is equal to:

P = 1/5 = 0.20

Now, for the experimental probability, we can see that out of 300 draws, 111 times he drew the card C.

The experimental probability is:

Pe = 111/300 = 0.37

You can see that the experimental probability is bigger than the theoretical one, this may happen for two things.

Not enough draws: as the number of draws, we should expect to see that the experimental probability gets closer and closer to the theoretical one.

The cards have some difference: There is a chance that card C has a difference with the other cards, and this difference makes that when Ryan draws a card has a bigger probability of drawing this one.

Kinda lost, can someone help me.

Answers

Answer:

Area: x^2 + 6x

Step-by-step explanation:

1. This figure resembles a parallelogram, with it's dimensions parallel to the point of congruency. Even if it wasn't a parallelogram however, you would get the basic idea of calculating it's area by height * length.

2. Knowing the dimensions to be ( x + 6 ) by x, you can multiply them through algebra as such: x ( x + 6 ) ⇒ x^2 + 6x

3. Answer: x^2 + 6x

Five friends bake ginger bread and subsequently meet up for a tasting session. Each one gives one of his ginger
breads to each other person. Then each person eats all of the ginger bread they were given. After that the
number of ginger breads halves. How many ginger breads did the five friends have to start with?

Answers

Answer:

The five friends had 10 fingers to start with; one had two each

Step-by-step explanation:

The statement says each gave one of not all of his ginger in the toasting session.

What’s the correct answer or this?

Answers

Answer:

Height = 35 x sin(55deg) = ~28.7 feet

Answer:

B

Step-by-step explanation:

Sin ∅ =opposite/HYPOTENUSE

Sin 55 =opposite/35

0.82×35=opposite

Opposite=28.7 feet

Giving brainliest to CORRECT answer.

Answers

Answer:

B) (-3,4)

Step-by-step explanation:

I graphed the function on the graph below to show you that vertex of the function.

If this answer is correct, please make me Brainliest!

The answer is B because it appears on my graphing calculator as this.

Jean Paul laying in his bathroom. The room measured 10 feet in length and 6 feet in width. What is the area of the bathroom.

Answers

Answer:

60 ft^2

Step-by-step explanation:

6x10

get off of the bathrrom floor jean you sicko

Answer:

6 x 10 = 60 ft.^2

(A = b h)

Step-by-step explanation:

Why is he laying on his bathroom floor/tub/whatever-

Area is base times height. (length times width, if you will)

10 x 6

      =60

Need help please no dumb answers I gotta turn it in in five min help a girl out please

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Answer:

boo just search the formula dud

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what are the dimensions for this triangle?

Answers

Answer:

2 and 2

Step-by-step explanation:

Parallel sides of rectangles are congruent, and because the other side of both rectangles is 2, the sides of the triangle are 2 because they share the side with the rectangle.

Determine the range of the following function {(-1,4)(0,6)(7,8)(2,-5)}

A) {-1,4,0,6}
B) {-1,0,7,8}
C) {4,6,8,-5}
D) {7,8,2,-5}

Answers

Answer:

C

Step-by-step explanation:

The range of a function is all of the y values of every point. In this case, that is 4, 6, 8, -5 (C). Hope that helps!

Answer:

The answer is C

Step-by-step explanation: 4 and 6 are the medium numbers. -5 and 8 and the lowest and highest nuumbers.

Find the area of the shape ​plssss help

Answers

ok so find the area of thesquare then triangles and then add them tiriange area is 1/2 times base times heightso 1/2 times 2 times 2 which is 4 divided by 2 which is 2 same with the other traingle so your total area for the traingles is 4. The area for the square is 2 times 2 which is 4. add them up yiouget the whole shape is 8 units squared Answer: 8 units squared

Step-by-step explanation:

The lengths of pregnancies are normally distributed with a mean of 250 days and a standard deviation of 15 days.

a. Find the probability of a pregnancy lasting 308 days or longer?








b. If we stipulate that a baby is premature if the length of the pregnancy is in the lowest 8% (8th percentile), find the length that separates premature babies from those who are not premature.

Answers

Answer:

a) 0.005% probability of a pregnancy lasting 308 days or longer

b) The pregnancy length that separates premature babies from those who are not premature is 229 days.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 250, \sigma = 15[/tex]

a. Find the probability of a pregnancy lasting 308 days or longer?

This is 1 subtracted by the pvalue of Z when X = 308. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{308 - 250}{15}[/tex]

[tex]Z = 3.87[/tex]

[tex]Z = 3.87[/tex] has a pvalue of 0.99995

1 - 0.99995 - 0.00005

0.005% probability of a pregnancy lasting 308 days or longer

b. If we stipulate that a baby is premature if the length of the pregnancy is in the lowest 8% (8th percentile), find the length that separates premature babies from those who are not premature.

The 8th percentile is X when Z has a pvalue of 0.08. So it is X when Z = -1.405.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.405 = \frac{X - 250}{15}[/tex]

[tex]X - 250 = -1.405*15[/tex]

[tex]X = -1.405*15 + 250[/tex]

[tex]X = 229[/tex]

The pregnancy length that separates premature babies from those who are not premature is 229 days.

Simplify 3 + 5(x - 4)

Answers

Answer:

5x - 17

Step-by-step explanation:

3 + 5x - 20

= 5x - 17

A pollen grain is 3/10 to the third power centimeters wide. In an illustration, the pollen grain is 6 centimeters 10 wide. How much larger is the illustration than the actual pollen?

Answers

Answer:

The illustration is approximately 226 times larder than the actual pollen grain.

Step-by-step explanation:

First of all, we have to write out the size of the actual pollen grain in a manner that is easy for us to work with.

This will be

[tex](\frac{3}{10}) ^{3}=0.027cm[/tex] wide

The original width of the pollen is 0.027 cm.

Next,

We can take the width of the illustration to be 6.10 cm  wide.

After this,

To get the magnification factor, we will have to use the formula

Magnification = illustrated size/ actual size

This will be the magnification = [tex]6.10/0.027[/tex] = 255.92 times

Hence, the illustration is approximately 226 times larder than the actual pollen grain.

What is the median for the given set of data?
[40, 54, 22, 30, 55, 13, 33}
A)
32
B)
33
C)
40
D)
42

Answers

B : 33
13 22 30 33 40 54 55

8 x
105 is how many times as great as 8 x 10-l?
10 4
10 6
10 -4
10 -6​

Answers

Answer:

10 6

................

The difference between the most hours of sleep and the least of these students was 2.5 hours. True or false?​

Answers

The correct anwer is False

Explanation

According to the graph, it can be seen that a student has four hours of sleep as the minimum number of hours of sleep; two students have six hours of sleep, four students have six and a half hours of sleep, four have seven hours of sleep, three have seven and a half hours of sleep, five have eight hours of sleep, and one has eight and a half hours of sleep as maximum hours of sleep. Therefore, it can be affirmed that the statement that the difference between the maximum amount and the minimum number of hours is two and a half hours is false because between four hours and eight and a half hours there are four and a half hours of difference. So, the correct answer is False.

How much did deshwan have withheld from his federal income tax

Answers

Answer:

$4465.71.

Step-by-step explanation:

Explanation: The amount of federal income tax withheld is on Box 2 of the WW2 form.

What is the value of sin(A)

Answers

Answer:

6/10

Step-by-step explanation:

A wall in Marcus’s bedroom is 8 2/5 feet high and 16 2/3 feet long. If he paints 1/2 of the wall blue, how many square feet will be blue?

Answers

77 feet^2

Explanation:

Area of the wall is

8 2/5 × 18 1/3

42/5 × 55/3

14/5 × 55/1

14/1 × 11/1 = 154 feet^2

The area we want is half of this

77 feet^2

Hope this helps and answer you question

In the equation m = k + 3, m is the:

Answers

Answer:

Step-by-step explanation:

m is the dependent variable; it represents the value of a linear function of k:

m = f(k) = k + 3

Children in 50 Households
Number of Children Number of
Households
0
5
1
11
2
13
3
10
4
9
5
2
Using a proportion, what can you infer about the number of households in her town that have more than thre
About 242 households have more than three children.
About 269 households have more than three children.
About 296 households have more than three children.
About 565 households have more than three children.

Answers

Answer:I think it’s 269 because when you do 1,350 divided by 50 it’s 27 then you add 9+2 to get 11/50 then you do 27x11 which gives you 270 and the closest answer to that is 269

Step-by-step explanation:

Answer:

About 296 households have more than three children.

Step-by-step explanation:

I got it right on edge

In a Monopoly market, a firm is a price maker since there are no close substitutes to the product. You are asked to find the company's Proft-Maximization point. Fixed Costs remains at $1,000.00. Calculate the revenue, profit (any), and costs on the graph,

Answers

ATC= TC/ Q
Avc= vc/q
Afc= Fc/ q
Mc= Change TC/ change q
Tc= vc+ fc
Vc= tc/ fc
Mr= change tr/ change q
P≠ mr

What do scientist mean by flattening the curve and why is it important?

Answers

Answer:

MRCORRECT has answered the question

Step-by-step explanation:

Inhibiting new infections to reduce the number of cases at any given time—known as "flattening the curve"—allows healthcare services to better manage the same volume of patients.

Answer:

I believe it means to slow down the virus spreading to other people and to stay safe, avoid contact, and wash your hands to stop too many people from going into the hospital.

Step-by-step explanation:

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