Which of the following best describes the least-squares line fit to the data shown in the plot? Py X (i) bo = 0, bị =-1 (ii) bo= -3, b₁ = 1 (iii) bo = -5, b₁ = 2 (iv) bo = −3, bị =−1 (v) bo = 0, b₁ = -3
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- Might we be able to predict life expectancies from birthrates? Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y = 82.17 -0.47x. Birthrate, x (number of births per 1000 people) 14.3 27.4 51.1 46.8 24.9 29.9 18.2 41.6 49.4 14.1 33.9 49.3 Send data to calculator Female life expectancy, y (in years) 75.6 70.5 58.2 59.0 73.3 62.7 73.6 65.2 62.4 74.3 67.0 53.9 Send data to Excel Female life expectancy (In years) Based on the sample data and the regression line, answer the following. 85+ 80+ 75+ 70+ 65 60 55+ 50 (a) From the regression equation, what is the predicted female life expectancy (in years) when the birthrate is 29.9 births per 1000 people? Round your answer to…A world wide fast food chain decided to carry out an experiment to assess the influence of income on number of visits to their restaurants or vice versa. A sample of households was asked about the number of times they visit a fast food restaurant (X) during last month as well as their monthly income (Y). The data presented in the following table are the sums and sum of squares. (use 2 digits after decimal point) ∑ Y = 393 ∑ Y2 = 21027 ∑ ( Y-Ybar )2 = SSY = 1720.88 ∑ X = 324 ∑ X2 = 14272 ∑ ( X-Xbar )2 = SSX = 1150 nx=8 ny=11 ∑ [ ( X-Xbar )( Y-Ybar) ] =SSXY=1090.5 PART A Sample mean income is Answer Sample standard deviation of income is Answer 90% confidence interval for the population mean income (hint: assume that income distributed normally with mean μ and variance σ2) is [Answer±Answer*Answer] 90% confidence interval for the population variance of income (hint: assume that income distributed normally with mean μ and variance σ2) is…Might we be able to predict life expectancies from birthrates? Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y= 82.15 – 0.47x. 00 Birthrate, x Female life expectancy, y (in years) (number of births per 1000 people) 40.4 65.2 85- 50.4 59.0 80+ 18.4 71.6 75- 26.5 69.9 70 32.0 64.5 65- 51.7 52.9 60- 34.4 67.2 14.6 75.9 50.1 45.8 59.2 49.9 62.1 Birthrate 73.7 26.2 (number of births per 1000 people) 73.7 14.4 Save For Later Submit Assignment Check 2 Accessibility O 2022 McGraw Hill LLC AN Rights Reserved. Terms of Use / Privacy Center DO 80 DIl 110 17 Da SO FA F4 esc F2 & delete %24 % 8 %23 6 7 3 4 7. U T K LA G S D Female life expectancy (in years)
- A company that manufactures computer chips wants to use a multiple regression model to study the effect that 3 different variables have on y, the total daily production cost (in thousands of dollars). Let B,, B,, and B, denote the coefficients of the 3 variables in this model. Using 22 observations on each of the variables, the software program used to find the estimated regression model reports that the total sum of squares (SST) is 485.84 and the regression sum of squares (SSR) is 229.91. Using a significance level of 0.10, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily production costs? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (a) State the null hypothesis H, for the test. Note that the alternative hypothesis H, is given. H, :0 H, : at least one of the independent variables is useful…Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where X is the age of the crab in months and Y is the predicted value of Y, the size of the male crab in cm. Y = 8.2052 + 0.5693X What is the value of Ý when a male crab is 21.7865 months old? Provide your answer with precision to two decimal places. Interpret the value of Ý. The value of Ý is the probability that a crab will be 21.7865 months old. the predicted number of crabs out of the 1,000 crabs collected that will be 21.7865 months old. the predicted incremental increase in size for every increase in age by 21.7865 months. the predicted size of a crab when it is 21.7865 months old.The following table shows the length, in centimeters, of the humerus and the total wingspan, in centimeters, of several pterosaurs, which are extinct flying reptiles. (A graphing calculator is recommended.) (a) Find the equation of the least-squares regression line for the data. (Where × is the independent variable.) Round constants to the nearest hundredth. y= ? (b) Use the equation from part (a) to determine, to the nearest centimeter, the projected wingspan of a pterosaur if its humerus is 52 centimeters. ? cm
- The least-squares regression equation is y=784.6x+12,431 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7962. In a particular region, 26.5 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $29,889. Is this income higher or lower than what you would expect? Why?Please help me better understand how to solve this word problem. In a study of 2000 model cars, a researcher computed the least-squares regression line of price (in collars) on horsepower. He obtained the following equation of: Price = -7000 + 170 X horsepower. Based on the least-squares regression line, what would we predict the cost of a 2000 model car with horsepower equal to 230 to be (assuming no extrapolation error)?An automotive engineer computed a least-squares regression line for predicting the gas mileage (mpg) of a certain vehicle from its speed in mph. The results are presented in the following Excel output: What is the regression equation? Intercept Speed R-Sq Coefficients 40.69 -0.22 0.588. Og = 40.69 0.22X Oy = 40.69 0.588X Oŷ = 0.22 + 40.69X Oy = 0.588 0.22X
- Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length. A least-squares regression on the data he collected produces the equation ŷ = 37.67 + 33.18x %3D where x is metatarsal-to-femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94. Construct an 80% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places. Lower limit: Upper limit:A biologist is interested in predicting the percentage increase in lung volume when inhaling (y) for a certain species of bird from the percentage of carbon dioxide in the atmosphere (x). Data collected from a random sample of 20 birds of this species were used to create the least-squares regression equation ŷ = 400-0.08x. Which of the following best describes the meaning of the slope of the least-squares regression line? (A) The percentage increase in lung volume when inhaling increases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (B) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on average, for every 1 percent increase in lung volume when inhaling. (C) The percentage increase in lung volume when inhaling decreases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (D) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on…An article gave a scatter plot, along with the least squares line, of x = rainfall volume (m³) and y data on rainfall and runoff volume (n = runoff volume (m³) for a particular location. The simple linear regression model provides a very good fit to 15) given below. The equation of the least squares line is y = -2.364 + 0.84267x, ² 0.976, and s = 5.21. = x 5 12 14 17 23 30 40 47 55 67 72 81 96 112 127 y 3 9 12 14 14 24 27 45 38 46 52 71 81 100 101 (a) Use the fact that s = 1.43 when rainfall volume is 40 m³ to predict runoff in a way that conveys information about reliability and precision. (Calculate a 95% PI. Round your answers to two decimal places.) Ŷ 28.25 1x ) m³ Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning. OYes, precise information is available because the resulting interval is very wide. 34.46 Yes, precise information is available because the resulting interval is very…
