Mathematics, 16.01.2020 16:31, emmeaw245

The table below shows the radius y, in inches, created by growing algae in x days: time (x) (days) 1 4 7 10 radius (y) (inches) 1 8 11 12 part a: what is the most likely value of the correlation coefficient of the data in the table? based on the correlation coefficient, describe the relationship between time and radius of the algae. [choose the value of the correlation coefficient from 1, 0.94, 0.5, 0.02.] (4 points) part b: what is the value of the slope of the graph of radius versus time between 4 and 7 days, and what does the slope represent? (3 points) part c: does the data in the table represent correlation or causation? explain your answer. (3 points)

Answers: 1

Show answers

Answers

PART A:
Given the table below showing the radius y, in inches, created by growing algae in x days.

Time (x) (days): 1 4 7 10
Radius (y) (inches): 1 8 11 12

We can find the find the correlation coeficient of the data using the table below:
$\begin{center}
\begin{tabular}
{|c|c|c|c|c|}
x & y & x^2 & y^2 & xy \\ [1ex]
1 & 1 & 1 & 1 & 1\\
4 & 8 & 16 & 64 & 32\\
7 & 11 & 49 & 121 & 77\\
10 & 12 & 100 & 144 & 120\\ [1ex]
\Sigma x=22 & \Sigma y=32 & \Sigma x^2=166 & \Sigma y^2=330 & \Sigma xy=230
\end{tabular}
\end{center}$

Recall that the correlation coefitient is given by the equation:
$r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{ \sqrt{(n\Sigma x^2-(\Sigma x)^2)(n\Sigma y^2-(\Sigma y)^2)} } \\ \\ = \frac{4(230)-(22)(32)}{ \sqrt{(4(166)-(22)^2)(4(330)-(32)^2)} } = \frac{920-704}{ \sqrt{(664-484)(1,320-1,024)}} \\ \\ = \frac{216}{ \sqrt{180(296)}} = \frac{216}{ \sqrt{53,280} } = \frac{216}{230.8} =0.94$

[Notice: even without using the formular to find the value of the correlation coeficient, it can be seen that the value of y strictly increases as the valu of x increases. This means that the value of the correlation coeficient is closer to +1 and from the options the value that is closest to +1 is 0.94]

From the value of the correlation coeffeicient, it can be deduced that the radius of the algae has a strong positive relationship with the time.

Recall the for the value of the correlation coeficient closer to +1, the relationship is strong positive, for the value closer to -1, the value is strong negative and for the values closer to zero, either way of zero is a weak positive if it is positive and weak negative if it is negative.

PART B:
Recall that the slope of a straight line passing through two points
(x_1,y_1)

and

is given by
$m= \frac{y_2-y_1}{x_2-x_1}$

Thus the slope of the graph of radius versus time between 4 and 7 days, [i.e. the line passes through points (4, 8) and (7, 11)] is given by
$m= \frac{11-8}{7-4}= \frac{3}{3} =1$

The value of the slope means that the radius of the algea grows by 1 inch evry day between day 4 and day 7.

PART C:
We can say that the data above represent both correlation and causationg.

Recall that correlation expresses the relationship between two variables while causation expresses that an event is as a result of another event.

From the information above, we have seen that there is a relationship (correlation) between the passing of days and the growth in the radius of the algae.

Also we can conclude that the growth in the radius of algae is a function of the passing of days, i.e. the growth in the radius of algae is as a result of the passing of days.

Therefore, the data in the table represent both correlation and causation.

answered: Guest

answer: c

because if you look at the chart you can see a pattern and compare it to the question he simplify out your

but i think the formula is f(x)=6x

49 points me! it's a multiple choice, but still show your work so i know you're right. you so so

answered: Guest

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:00, goodygoodgirlygirl

If the measure of angle 1 is 110 degrees and the measure of angle 3 is (2 x+10 degree), what is the value of x?

Answers: 2

continue

Mathematics, 21.06.2019 18:10, lulustar13

Television sizes are based on the length of the diagonal of the television's rectangular screen. so, for example, a 70-inch television is a television having a diagonal screen length of 70 inches. if a 70 inch television's diagonal forms a 29°angle with the base of the screen, what is the vertical height (1) of the screen to the nearest inch? 70 inhin

Answers: 3

continue

Mathematics, 21.06.2019 19:20, ayeofaygo5168

The fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. round the answers to 4 decimal places. less-than-or-equal-to p less-than-or-equal-to (b) calculate a 95% upper confidence bound on the fraction of defective circuits. round the answer to 4 decimal places. p less-than-or-equal-to

Answers: 3

continue

Mathematics, 21.06.2019 20:20, redbeast677

The polynomial 10x3 + 35x2 - 4x - 14 is factored by grouping. 10x3 + 35x2 - 4x - 14 5x )-20 what is the common factor that is missing from both sets of parentheses?

Answers: 2

continue

Do you know the correct answer?

The table below shows the radius y, in inches, created by growing algae in x days: time (x) (days)...