Round 4.265 to the nearest hundredth

Find the correlation coefficient of the line of best fit for the points (-3,-40), (1,12), (5,72), (7,137). Explain how you guy y

vodka [1.7K]

Answer:

r = 0.9825; good correlation.

Step-by-step explanation:

One formula for the correlation coefficient is

$r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{n\left [\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}$

The calculation is not difficult, but it is tedious.

1. Calculate the intermediate numbers

We can display them in a table.

x y xy x² y²

-3 -40 120 9 1600

1 12 12 1 144

5 72 360 25 5184

7 137 959 49 18769

Σ = 10 181 1451 84 25697

2. Calculate the correlation coefficient

$r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{4\times 1451 - 10\times 181}{\sqrt{[4\times 84 - 10^{2}][4\times25697 - 181^{2}]}}\\\\= \dfrac{5804 - 1810}{\sqrt{[336 - 100][102788 - 32761]}}\\\\= \dfrac{3994}{\sqrt{236\times70027}}\\\\= \dfrac{3994}{\sqrt{16526372}}\\\\= \dfrac{3994}{4065}\\\\= \mathbf{0.9825}$

The closer the value of r is to +1 or -1, the better the correlation is. The values of x and y are highly correlated.

3 0

1 year ago

A financial advisor tells you that you can make your child a millionaire if you just start saving early. You decide to put an eq

Blababa [14]

Answer:

$12159 per year.

Step-by-step explanation:

If I invest $x each year at the simple interest of 7.5%, then the first $x will grow for 35 years, the second $x will grow for 34 years and so on.

So, the total amount that will grow after 35 years by investing $x at the start of each year at the rate of 7.5% simple interest will be given by

$x( 1 + \frac{35 \times 7.5}{100}) + x( 1 + \frac{34 \times 7.5}{100}) + x( 1 + \frac{33 \times 7.5}{100}) + ......... + x( 1 + \frac{1 \times 7.5}{100})$

= $35x + \frac{x \times 7.5}{100} [35 + 34 + 33 + ......... + 1]$

= $35x + \frac{x \times 7.5}{100} [\frac{1}{2} (35) (35 + 1)]$

{Since sum of n natural numbers is given by $\frac{1}{2} (n)(n + 1)$ }

= 35x + 47.25x

= 82.25x

Now, given that the final amount will be i million dollars = $1000000

So, 82.25x = 1000000

⇒ x = $12,158. 05 ≈ $12159

Therefore. I have to invest $12159 per year. (Answer)

5 0

2 years ago

A dartboard has 8 sections of equal area. The letters represent colors red (R), yellow (Y), blue (B), and green (G). Complete th

Alla [95]

Since the sum of all probabilities of all all elementary events will always be equal to 1. Furthermore, the probabilities of all mutually exclusive set of events that is part of the entire sample space will always be total of 1.

So in the problem, the answer is 1/8.
1/8 for red + 3/8 for green + 3/8 for yellow + 1/8 for blue = 8/8 or 1.

4 0

2 years ago

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How many 4/5 cup servings are in 4/9 of a cup of yogurt

kolbaska11 [484]

For this question, you need to understand how to divide fractions.First we line up our fractions appropriately:
4/9 ÷ 4/5 = ? (You want to divide 4/9 by 4/5)
4/9 × 5/4 = ? (Now we use the reciprocal of 4/5 and multiply instead of divide)
4 x 5 = 20 and 9 x 4 = 36. (Cross multiply.)
20/36 = 5/9. (Simplify to lowest terms.)
So, 4/9 divided by 4/5 is 5/9!But 5/9 is more than 4/9, so the answer is 0 :PCorrect me if I'm wrong.

5 0

1 year ago

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Which value of y would make O P is parallel to L N? 16 24 32 36

natita [175]

Answer:

Step-by-step explanation:

Triangle proportionality theorem,

$\frac{MO}{OL}=\frac{MP}{PN}\\\\\frac{28}{14}=\frac{y}{18}\\\\\frac{28}{14}*18=y\\\\y=\frac{28}{7}*9\\\\y=4*9\\\\y=36$

8 0

1 year ago

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