Suppose you have a Simple population regression function describe as follows Y₁ = Bo + B₁X₁ + εi derive the ordinary least squares estimator of the coefficients.
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- If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
- The equation Y= α+ βx+ε describes a population regression line. Which of the statements regarding this equation is true. A. ε is the coefficient of standard deviation B. α,β are sample statistics that can be calculated by the ordinary least squares method C. α,β are usually unknown since they are population quantities D. None of the statements above are trueFind the equation for the least squares regression line of the data described below. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. Round your answers to the nearest thousandth. y = L SubmitMight 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=83.86-0.52x. Birthrate, x Female life expectancy, y (in years) (number of births per 1000 people) 34.4 67.3 19.6 72.9 49.2 58.8 XX 39.4 63.8 28.0 73.3 50.3 53.9 14.1 77.3 15.5 73.3 45.0 57.8 30.8 63.2 50.6 61.8 26.0 73.3 Send data to calculator V Based on the sample data and the regression line, answer the following. (a) From the regression equation, what is the predicted female life expectancy (in years) when the birthrate is 30.8 births per 1000 people? Round your answer to one or more decimal places. (b) From the regression equation, what is the…
- In Step 2: Construct an estimated simple linear regression model how did you come up with the column X*X ?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 = 82.76 -0.50x. Birthrate, x (number of births per 1000 people) 20.5 39.4 46.5 52.8 26.5 35.2 47.1 49.1 23.6 31.9 15.6 13.9 Send data to calculator V Female life expectancy, y (in years) 72.7 65.1 58.1 57.9 72.2 67.5 60.8 53.3 73.3 64.0 72.1 75.0 Based on the sample data and the regression line, complete the following. Female life expectancy (in years) 85 80+ 75- 70- 65 60- 55+ 50+ x xx 10 15 20 25 30 x than (b) According to the regression equation, for an increase of one (birth per 1000 people) in birthrate, there is a corresponding decrease of how many…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)
