**Calculation of Pearson Correlation Coefficient**To find the Pearson correlation coefficient \( r \) for the correlation between the number of hours students slept the night before a test and their test score, follow the formula provided. Round your answer to two decimal places.### Data Table| Hours Slept (X) | Test Score (Y) ||-----------------|----------------|| 8 | 83 || 7 | 86 || 7 | 74 || 8 | 88 || 6 | 76 || 5 | 63 || 7 | 90 || 4 | 60 || 9 | 89 || 7 | 81 |### Formula\[ r = \frac{N \sum XY - (\sum X)(\sum Y)}{\sqrt{[N \sum X^2 - (\sum X)^2][N \sum Y^2 - (\sum Y)^2]}} \]### Given Values- \( \sum X = 68 \)- \( \sum Y = 790 \)- \( \sum X^2 = 482 \)- \( \sum Y^2 = 63,432 \)- \( \sum XY = 5,497 \)### Explanation- \( N \) is the number of data points (students).- \( \sum X \) and \( \sum Y \) are the sums of the hours slept and test scores respectively.- \( \sum X^2 \) and \( \sum Y^2 \) are the sums of squares of the hours slept and test scores respectively.- \( \sum XY \) is the sum of the product of each pair of x and y values.Use these values to calculate the Pearson correlation coefficient \( r \) using the formula above.

Answered: Find the Pearson r(correlation…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Use Pearson’s Product Moment correlation coefficient (r) to find the relationship between the independent variable (hour spent in studying) to the dependent variable (achievement score). Complete the table below and follow the steps in solving Pearson’s Product Momentcorrelation coefficient (r). Round off your answer into two decimal places.
Compute the correlation coefficient between the price of eggs and the price of milk. Round the answer to at least three decimal places.
Kim wants to determine a 90 percent confidence interval for the true proportion p of high school students in the area who attend their home basketball games. Out of n randomly selected students she finds that that exactly half attend their home basketball games. About how large would n have to be to get a margin of error less than 0.02 for p?
The number of hours 13 students spent studying for a test and their scores on that test: Hours spent studying(x) Test score (y) 0 40 1 41 2 51 3 48 4 64 4 69 5 73 5 75 6 68 6 93 7 84 7 90 8 95 Using 5% level of significance, is there a significant relationship between hours spent studying and test score. What is the coefficient of determination? Leave answers in 4 decimal places.
year, X tuition, y The data in the chart show the cost of tuition at a state university for the years 1997-2001. Fit a regression line to the data, where x is the number of years after 1997 Then find the coefficlent of correlation Finally, use the regression 2. (1999) 11,006 ine to predict the cost of tuition in 2004 2007, and 2010. 0. (1997) 1. (1998) 10,369 9743 3. (2000) 4. (2001) 11.486 12.077 Choose the correct regression line OA. y9779 2x+578 5 OC. y578 5x-97792 OB y=578.5x +9779 2 OD. y=9779.2
A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below. Time 14 30 11 29 25 6 26 Money 62 97 39 118 76 18 83 Find the correlation coefficient: r = ________ (Round to 2 decimal places) The p-value is: ________ (Round to 4 decimal places)
Forest Fires and Acres Burned Numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned for 7 recent years are shown. Number of fires x 72 69 58 47 84 62 57 Number of acres burned y 74 71 60 49 86 64 59 Send data to Excel The correlation coefficient for the data is r= 1 and a=0.05. Should regression analysis be done? The regression analysis should not be done. The regression analysis should be done. Find the equation of the regression line. y'=a+bx a b. Find y' when x=55. y' = %3D to
Using the data in the table below, find the Rank (R) and Product Moment (r) Correlation Coefficient. Personality (1) Behaviour (y) 5 8 6 7 7 5 7 5 8 4 9 4 9 5 9 6 8 6 9
Would you say the correlation is positive or negative? positive O negative (c) Use a calculator to verify that Σ * Ex=61, Ex Computer. (Round your answer to four decimal places.) 0.9802 Need Help? cloudy = 1007, x2 = 1007, Σy = 634, Σ Master It As x increases from 3 to 23 months, does the value of rimply that y should tend to increase or decrease? Explain y O Given our value of r, y should tend to decrease as x increases. Given our value of r, y should tend to increase as x increases. Given our value of r, we can not draw any conclusions for the behavior of y as x increases. O Given our value of r, y should tend to remain constant as x increases. Q Search = 14 mmm 90,298, and Exy = 9,315. hp 9 |99+ X
Forest Fires and Acres Burned Numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned for 6 recent years are shown. Number of fires x 69 58 62 84 47 72 Number of acres burned y 62 42 19 15 26 42 Send data to Excel The correlation coefficient for the data is =r−0.054 and =α0.01 . Should regression analysis be done? The regression analysis should not be done. The regression analysis should be done. Find the equation of the regression line. =y′+abx =a =b Find y′ when =x60 . =y′
Homework Q2: Find the Pearson correlation coefficient Person Age (x) Income (y) (xy) (x²) (y²) 1 20 1500 30000 400 2250000 2 30 3000 90000 900 9000000 3 40 5000 200000 1600 25000000 4 50 7500 375000 2500 56250000 Total 140 17000 695000 5400 92500000 23

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