Explain the distinction between regression and correlation. Calculate the coefficient of correlation from the following data by the method of rank differences: Rank of X 10 4 2 5 8 5 Rank of Y 10 6. 8 5
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A: From the given information, The coefficient of determination, r2= 0.862 Slope of the regression…
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A: The following information has been provided: The coefficient of determination is R2=0.784. The slope…
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A: r2=0.837 slope=m=3.26
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A: Given r=0.986
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A: Answer:----. Date:----12/10/2021 r = -0.984 So, r^2 = 0.968256
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Q: Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of…
A: xy186.7174.9190.1185.7173.9178.6193.2189.8181.7189.0171.6182.3188.0187.9157.4175.1201.8190.3160.1173…
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A: coefficient of variation It is a standardized dispersion measure of the distribution of probability.
Q: Use the value of the linear correlation coefficient to calculate the coefficient of determination.…
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Q: What information does a regression coecient provide that a correlation does not?
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Q: Use the value of the linear correlation coefficient to calculate the coefficient of determination.…
A: Given : Correlation coefficient = r = 0.926
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- Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims. x 3 7 15 32 75 y 40 35 30 26 18 (a) Make a scatter diagram of the data and visualize the line you think best fits the data. Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website. (b) Would you say the correlation is low, moderate, or strong? positive or negative? strong and negative moderate and negative strong and positive low and negative low and positive moderate and positive (c) Use a calculator to verify that Σx = 132, Σx2 = 6932, Σy = 149, Σy2 = 4725, and Σxy = 2997. Compute r. (Round your answer to three decimal places.)r = As x increases, does the value of r imply that y should tend to increase or decrease? Explain. Given our value of r, we cannot draw any conclusions for the behavior of y as x increases. Given our value of r, y should tend to…The numbers of pass attempts and passing yards for seven professional quarterback for a recent year are listed in the table below. Round all answers to the nearest 1000th. Pass attempts (x) 449 565 528 197 670 351 218 Passing Yards (y) 3265 4018 3669 1141 5177 2362 1737 Calculate the sample correlation coefficient, r. Describe the type of correlation coefficient and interpret the correlation in the context of the data. Find the equation of the regression line for the data. Use the regression equation to predict the average number passing yards if the pass attempts are 250.Let x be the weight of a car (in hundreds of pounds), and let y be the miles per gallon (mpg). Suppose a car weighs 3800 pounds. What does the data forecast for the miles per gallon expected? x= 27 44 32 47 23 40 34 52 y= 30 19 24 13 29 17 21 14 State the correlation coefficient and state the regression lin equation.
- A study is conducted concerning the prices for books and the number of pages that each book contains. The following data are collected. Pages (X) Prices (Y) is dollars 500 700 750 590 540 650 480 7 7.5 9. 7 7.5 7 (a) Compute the correlation coefficient and comment on its value. (b) Find the regression line. (c) Interpret the regression line. (d) Predict the book price when the number of pages is equal to 575. Give a 99% confidence interval for your prediction in (d).´A study is conducted to determine the relationship between a driver’s age and the number of accidents they have over a year. Find the correlation coefficient, and the linear regression line. Predict the number of accidents a 28 year old driver would have. Driver’s age (x) 16 24 18 17 23 27 32 No. of accidents (y) 3 2 5 2 0 1 1Explain the relationship between correlation and regression. What are the practica applications of them?
- Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relations of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity in centimeters) of the father's oldest son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given are the products of the heights of fathers and heights of sons for each of the fifteen pairsJanice Carilllo a gainesville florida real estate developer has devised a regression model to help determine residential housing prices in northeastern florida. The model was developed using recent sales in a particular neighborhood. The price (y) of the house is based on the size (square footage =X) of the house. The model is : Y=12,973+37.65X The coefficient of correlation for the model is 0.73 a) Using the above model the selling price of a house that is 1760 square feet= $79,237 b) a 1760 square foot house recently sold for $92,000 which is dfiferent than predicted value. This is possible as the forecast represents average value. c) To make this model more realistic additional quantitative variables that could be included in multiple regression model are =The age of the house the number of bedrooms and the size of the lot d) For the given model the value of the coefficient of determination= [__] (round your response to three decimal places)The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r= - 0.972. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y= - 0.0070x + 44.4405. Complete parts (a) and (b) below. Click the icon to view the data table. ..... (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is %. (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. % of the variance in is by the linear model. Data Table (Round to one decimal p Full data set gas mileage Miles per Weight (pounds), x Weight (pounds), x Miles per Gallon, y Car Car Gallon, y…
- The data show the number of viewers for television stars with certain salaries. Find the regression equation, letting salary be the independent (x) variable. Find the best predicted number of viewers for a television star with a salary of $6 million. Is the result close to the actual number of viewers, 8.9 million? Use a significance level of 0.05. Salary (millions of $) Viewers (millions) Click the icon to view the critical values of the Pearson correlation coefficient r. 98 3.5 3 7 13 12 13 10 2 6.8 6.3 10.2 8.5 4.4 1.8 2.7 What is the regression equation? y=+x (Round to three decimal places as needed.) What is the best predicted number of viewers for a television star with a salary of $6 million? The best predicted number of viewers for a television star with a salary of $6 million is million. (Round to one decimal place as needed.) Is the result close to the actual number of viewers, 8.9 million? O A. The result is very close to the actual number of viewers of 8.9 million. O B. The…Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given is the product of the father's height and the son's height for each of the fifteen pairs. (These products, written in the column labelled "xy", may aid in calculations.) Height of father, x (in centimeters) 176.6 181.3 171.6 158.3 181.5 190.5 161.2 191.2 175.9 Height of son, y (in centimeters) 173.4 188.9 180.7 175.0 176.3 189.2 168.5 194.8 179.5 191.3 171.2 200.0 170.1 192.2 162.0 186.8 184.9 Send data to calculator 190.9 172.1 176.4…Use the following to answer the question: ŷ : = −3x + 13.9 with R² = 34%. Which best describes the correlation? No linear relationship Weak positive linear relationship O Moderate negative linear relationship O Moderate positive linear relationship Weak negative linear relationship
