b) Show that by using least square estimation, a and ß can be determined respectively as:nΣα -(x; − x)(y; − y)i=1ВnΣ(x₁ - x)²i=1a=y-Bxwhere x, and y, are respectively the observed income and trips of household i, x andy are the average income and number of trips among all households, n is the totalnumber of households surveyed.Please include and show all your working steps in detail.

Answered: Image /qna-images/answer/80574629-807e-4098-99d5-0b65e0767e66.jpg

Answered: b) Show that by using least square…

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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It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:x5.756.257.258.259.25y2218786795What percentage of the variation in y cannot be explained by the corresponding variation in x and the least-squares line?
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.00 5.25 5.75 6.75 7.00 y 8 15 13 49 71 Find the equation of the least squares line . Round a and b to three decimal places. Find the correlation coefficient r for the elevation and percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation
Let x represent the hemoglobin count (HC) in grams per 100 milliliters of whole blood. The distribution for HC is approximately normal with μ = 14 for healthy adult women. Suppose that a female patient has taken 12 laboratory blood samples in the last year. The HC data sent to her doctor is listed below. We would like to know if the data indicates this patient has significantly high HC compared to the population. 14,19,16,14,19,19,14,21,17,17,14,17 Give the p-value and interpret the results. a) p = 0.0012; Based on 5% significance level, I will reject the null hypothesis and conclude this patient has a high HC level. b) p = 0.0012; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. c) p = 0.0023; Based on 5% significance level, I will reject the null hypothesis and conclude this patient has a high HC level. d) p = .1053; Based on 5% significance level, I will fail to reject the null hypothesis and…
A manager wishes to determine the relationship between the distance (in hundreds of miles) the manager's sales representatives travel per month and the amount of sales (in thousands of dollars) per month. Find the standard error of estimate, Se given that ý = 3.5x + 31.388889 %3D 15 8 Miles Travele1,r Sales, y 13 11 10 3 14 76 68 65 42 38 84 82 63 48 E= 81; y = 566 a² = 913; y² = 37886 2 xy = 5738 OS, = 2.025 S = 2.296 OS. = 1.895 Se = 1.735 S. = 2.446
Consider the following data on the number of minutes (x) that 10 persons spent on social media during office hours and their productivity level (y): Xi 10 29 54 63 70 76 88 91 108 118 Yi 92 72 59 50 49 48 38 25 14 9 A linear model was fitted using the statistical software R, producing the following output: Coefficients: (Intercept) 98.81082 -0.75263 Estimate Std. Error t value Pr(>|t|) 29.8 1.74e-09 *** -17.6 1.1le-07 *** 3.31574 0.04277 Signif. codes: 0 ***' 0.001 **** 0.01 0.05 .' 0.1 1 Residual standard error: 4.304 on 8 degrees of freedom Multiple R-squared: 0.9748, F-statistic: 309.7 on 1 and 8 DF, Adjusted R-squared: p-value: 1.11e-07 0.9717 (a) Obtain the equation of the estimated regression line. (b) Interpret the slope coefficient. (c) Discuss whether the simple linear regression model obtained does a good job of explaining observed variation in productivity level. (d) Perform a model utility test using a = 0.01. Use an appropriate P-value from the output given. (Note: R uses…
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.75 6.25 6.75 7.75 8.25 y 31 26 38 74 72 Find the value of the coefficient of determination r2. Group of answer choices
Let x represent the hemoglobin count (HC) in grams per 100 milliliters of whole blood. The distribution for HC is approximately normal with μ = 14 for healthy adult women. Suppose that a female patient has taken 12 laboratory blood samples in the last year. The HC data sent to her doctor is listed below. We would like to know if the data indicates this patient has significantly high HC compared to the population. 22,17,20,17,17,14,16,21,15,21,15,22 Give the p-value and interpret the results. a) p = .1053; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. b) p = .0562; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. c) p = 0.0003; Based on 5% significance level, I will fail to reject the null hypothesis and conclude this patient does not have a high HC level. d) p = 0.0003; Based on 5% significance level, I will reject the…
We will fit a least-squares line y = Bo+ B1x to the data in the following table using x as the independent variable. 3 6 7 9 12 y 1 5 9 The mean values are: x=7 and y=5. Answer the following questions (select correct/closest choices). 1) Estimated value of the slope, B, is O 0.905 O 0.840 O 0.760 1.333 2) Estimated value of the intercept, Bo is O 1.333 -1.200 -0.320 O 3.200 3) The fitted y value when x=6 is O 3.816 O 4.664 4.240 3.604 4) The residual when x=6 is O 0.646 O 0.760 0.684 0.836 LO
The following data pertain to x, the amount of fertil-izer (in pounds) that a farmer applies to his soil, and y, his yield of wheat (in bushels per acre): xy xy xy112 33 88 24 37 2792 28 44 17 23 972 38 132 36 77 3266 17 23 14 142 38112 35 57 25 37 1388 31 111 40 127 2342 8 69 29 88 31126 37 19 12 48 3772 32 103 27 61 2552 20 141 40 71 1428 17 77 26 113 26 Assuming that the data can be looked upon as a randomsample from a bivariate normal population, calculate rand test its significance at the 0.01 level of significance.Also, draw a scattergram of these paired data and judgewhether the assumption seems reasonable.
The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. Year03691215 Retail Sales85.851108.426141.781169.256202.297222.266 Let y be the retails sales in billions of dollars in x years since 1995. A linear model for the data is y=9.44x+84.182 A) Use the above scatter plot to decide whether the line of best fit, fits the data well. The function is a good model for the data.The function is not a good model for the data B) To the nearest billion, estimate the retails sales in the U. S. in 2011. billions of dollars. C) Use the equation to find the year in which retails sales will be $240 billion. .
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.75 6.75 7.75 8.50 9.25 y 27 16 46 62 95 What percentage of the variation in y cannot be explained by the corresponding variation in x and the least-squares line? Round your answer to the nearest tenth of a percent. 3.4% 18.4% 81.6% 9.7%
Show necessary calculation/justification for each answer. a) In regression analysis, the residuals represent the:a. difference between the actual y values and their predicted values.b. difference between the actual x values and their predicted values.c. square root of the slope of the regression line.d. change in y per unit change in x. b) The least squares method for determining the best fit minimizes:a. total variation in the dependent variableb. sum of squares for errorc. sum of squares for regressiond. All of these choices are true. c) The regression line has been fitted to the data points (4, 8), (2, 5), and (1, 2).The sum of the squared residuals will be:a. 7b. 15c. 8d. 22

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