х3031117169341321276953Ex = 74; Ey = 584; Ex? = 1,404; Ey? = 70,840; Exy = 9,584%3D(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.)x = 12.33y = 97.33b = 4.847ý = 37.567 x+4.847(b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram.УУ2002001501501001005050101520 2535510152535200200150-150-10010050101520253035101520253035 (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)(d) For a neighborhood with x = 21% change in population in the past few years, predict the change in the crime rate (per 1000 residents). (Round your answer to one decimal place.)crimes per 1000 residents

Answered: Image /qna-images/answer/2a7cae99-fd7f-43bd-a6be-c8d50e0b431f.jpg

Answered: х 30 3 11 17 169 34 132 127 69 53 Ex =…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.4: Mathematical Models And Least Squares Analysis

Problem 39E

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Zipfs Law The following table shows U.S cities by rank in terms of population and population in thousands. City Rank r Population N New York 1 8491 Chicago 3 2722 Philadelphia 5 1560 Dallas 9 1280 Austin 11 913 San Francisco 13 852 Columbus 15 836 A rule known as Zipfs law tells us that it is reasonable to approximate these data with a power function. a Use power regression to express the population as a function of the rank. b Plot the data along with the power function from part a. c Phoenix is the sixth largest city in the United States. Use your answer from part a to estimate population of Phoenix. Round your answer in thousands to the nearest whole number. Note: The actual population is 1537 thousand.
Further Verification of Newtons Second LawThis exercise represents a hypothetical implementation of the experiment suggested in the solution of part 6 of Example 3.7. A mass of 15 kilograms was subjected to varying accelerations, and the resulting force was measured. In the following table, acceleration is in meters per second per second, and force is in newton. Acceleration Force 8 120 11 165 14 210 17 255 20 300 a. Construct a table of differences and explain how it shows that these data are linear. b. Find a linear model for the data. c. Explain in practical terms what the slope of this linear model is. d. Express, using functional notation, the force resulting from an acceleration of 15 meters per second per second, and then calculate that value. e. Explain how this experiment provides further evidence for Newtons second law of motion.
(a) Find the equation of the least-squares line for the data. (Round all numerical values to two decimal places.) y= ?
When a stone is dropped in a pond, ripples are formed and travel in concentric circles away from where the stone was dropped. The equation of the least-squares regression line is log (area) = 0.490 +2.004 log (time) . What is the predicted area of the circle, in cm2, 4 seconds after the stone is dropped? 49.72 cm2 199.43 cm2 311.89 cm2 1854.10 cm2
a)Find the equation of the least-squares regression line for the data. (Where x is the independent variable.) Round constants to the nearest hundredth. b)Use the equation from part (a) to determine, to the nearest centimeter, the projected wingspan of a pterosaur if its humerus is 53 centimeters.
When a stone is dropped in a pond, ripples are formed and travel in concentric circles away from where the stone was dropped. The equation of the least-squares regression line is (picture attached) What is the predicted area of the circle, in cm2, 4 seconds after the stone is dropped? 49.72 cm2 199.43 cm2 311.89 cm2 1854.10 cm2
E) Use the original least squares line to predict the gestation period of a human being, assuming a longevity of 75 years. F) why does your answer for part (e) differ so much from the average gestation period of a human (280 days)?
A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: ˆyy^=a+bxa=-1.778b=0.143 (a) Write the equation of the Least Squares Regression line of the formˆyy^= + x(b) Which is a possible value for the correlation coefficient, rr? -0.853 0.853 -1.931 1.931 (c) If a country increases its life expectancy, the happiness index will decrease increase
a) Determine the least squares regression equation for the height of the ball over time. b) Find the correlation coefficient, r-value, of the line. Round your answer to the nearest thousandth. c) Predict the height of the ball after 11 seconds. ____ feet
For a sample of 15 rural counties in one state, a researcher has collected information about the rate of deaths due to traffic accidents per 1,000,000 population and the percentage of the population which consists of males, age 16 to 25. For these variables, find the least squares regression line and compute r and r squared. Write a sentence or two summarizing and explaining your results. RATE OF % OF POPULATION County Traffic Deaths Young Males County Traffic Deaths Young Males A 15 4 B 16 5 C 22 10 D 23 9 E 20 8 F 25 11 G 18 2 H 15 6 I 19 12 J 10 3 K 9 2 L 18 15 M 15 9 N 24 16 O 9 3
Advertising share x and market share y fir a particular brand of cigarettes were sampled at ten randomly selected year. Summary information is: n = 10, Ex = .688, Ex2 = .050072, Ey =.835, Ey2 = 0.079491, Exy = .060861 a) Compute the least squares regression line b) Find the coefficient of determination r2 and explain what it means in the context of this problem. c) Compute a 90% prediction interval for market share when advertising share is .07(7%)
The USPS is studying the relationship between the distance a shipment had to travel and the length of time, in days, it takes to arrive at its destination. They select a random sample of 20 shipments to look at. Determine the standard error estimate. (Round your answer to three decimal places) (Hint: your least squares regression line is y-hat = -7.1 + (0.02139 * x))

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