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The time it takes for a planet to complete its orbit around a particular star is called the? planet's sidereal year. The siderea

BartSMP [9]

Answer:

(a) See below

(b) r = 0.9879

(c) y = -12.629 + 0.0654x

(d) See below

(e) No.

Step-by-step explanation:

(a) Plot the data

I used Excel to plot your data and got the graph in Fig 1 below.

(b) Correlation coefficient

One formula for the correlation coefficient is

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

The calculation is not difficult, but it is tedious.

(i) Calculate the intermediate numbers

We can display them in a table.

x y xy x² y²

36 0.22 7.92 1296 0.05

67 0.62 42.21 4489 0.40

93 1.00 93.00 20164 3.46

433 11.8 5699.4 233289 139.24

887 29.3 25989.1 786769 858.49

1785 82.0 146370 3186225 6724

2797 163.0 455911 7823209 26569

3675 248.0 911400 13505625 61504

9965 537.81 1545776.75 25569715 95799.63

(ii) Calculate the correlation coefficient

$r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{9\times 1545776.75 - 9965\times 537.81}{\sqrt{[9\times 25569715 -9965^{2}][9\times 95799.63 - 537.81^{2}]}} \approx \mathbf{0.9879}$

(c) Regression line

The equation for the regression line is

y = a + bx where

$a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\= \dfrac{537.81\times 25569715 - 9965 \times 1545776.75}{9\times 25569715 - 9965^{2}} \approx \mathbf{-12.629}\\\\b = \dfrac{n \sum xy - \sum x \sum y}{n\sum x^{2}- \left (\sum x\right )^{2}} - \dfrac{9\times 1545776.75 - 9965 \times 537.81}{9\times 25569715 - 9965^{2}} \approx\mathbf{0.0654}\\\\\\\text{The equation for the regression line is $\large \boxed{\mathbf{y = -12.629 + 0.0654x}}$}$

(d) Residuals

Insert the values of x into the regression equation to get the estimated values of y.

Then take the difference between the actual and estimated values to get the residuals.

x y Estimated Residual

36 0.22 -10 10

67 0.62 -8 9

93 1.00 -7 8

142 1.86 -3 5

433 11.8 19 - 7

887 29.3 45 -16

1785 82.0 104 -22

2797 163.0 170 - 7

3675 248.0 228 20

(e) Suitability of regression line

A linear model would have the residuals scattered randomly above and below a horizontal line.

Instead, they appear to lie along a parabola (Fig. 2).

This suggests that linear regression is not a good model for the data.

4 0

3 years ago

The ages of undergraduate students in a state

Elan Coil [88]

The percent of students that are aged 19 years or more is determined as 84%.

<h3>One standard deviation below the mean</h3>

In a normal distribution curve 1 standard deviation below the mean is defined as follows;

1 std below mean : M - d = 16%

M - d = 20.6 yrs - 1.3 yrs = 19.3 years ≈ 19 years

19 years or more will occur at (M - d) + (M) + (M + 2d) = 100% - (M - d)

= 100% - 16%

= 84%

Thus, the percent of students that are aged 19 years or more is determined as 84%.

Learn more about normal distribution here: brainly.com/question/4079902

#SPJ1

7 0

2 years ago

A radioactive isotope that was originally 275 grams has decayed to 150 grams. the equation shown can be used to calculate the nu

k0ka [10]

Answer: 4.4 years

Step-by-step explanation:

3 0

3 years ago

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Rus_ich [418]

Answer:8.6

Step-by-step explanation:

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3. 1 + sec2x sin2x = sec2x

IgorLugansk [536]

Answer:

Answer is on pic

Step-by-step explanation:

I hope it's helpful!

7 0

3 years ago