From the following data estimate the valuts of Y for given values of X with the help of the method of least squares. Also calculate the standard error of the estimates of Y, and the value of the coefficient of correlation by using the standard error of the estimates of Y and the standard deviation of the original values of Y. Values of X 16 15 35 40 50 Values of Y 100 90 110 80 120

From the following data estimate the valuts of Y for given values of X with the help of the method of least squares. Also calculate the standard error of the estimates of Y, and the value of the coefficient of correlation by using the standard error of the estimates of Y and the standard deviation of the original values of Y. Values of X 16 15 35 40 50 Values of Y 100 90 110 80 120

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 3E: For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a...

See similar textbooks

Similar questions

Respiratory 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.
For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.
The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02
Interpret the least squares regression line of this data set. 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. The correct least squares regression line for the data set is: y = 8.116x + 273.273 Use it to complete the following sentence: The least squares regression line predicts an additional annual rainfall if the average temperature of coastal waters increases by one degree millimetres of Celsius.
Suppose a car's city miles per gallon rating can be determined by the car's weight. The means and standard deviations of these variables and the correlation coefficient between them are reported in the following table. Determine the coefficients of the least squares line for predicting a car's miles per gallon rating from its weight. Report the equation of this line. 2 decimals for "a" and 5 decimals for "b"
When a least squares line is fit to the 8 observations in the fuel consumption data, we obtain SSE = 3.264. Calculate s? and s. (Round your answers to 3 decimal places.)
When a least squares line is fit to the 11 observations in the service time data, we obtain SSE = 334.1354. Calculate s and s. (Round s2 to 4 decimal places. Round s to 5 decimal places.)
The least squares regression line for the cost of a diamond necklace from a department store (y, in dollars) in the year xyears since 2000 is given by yˆ=1823+314x. Interpret the y-intercept of the least squares regression line. Select the correct answer below: The predicted cost of a diamond necklace from the department store is expected to increase $314 per year after the year 2000. The predicted cost of a diamond necklace from the department store in the year 2000 is $1823. The predicted cost of a diamond necklace from the department store in the year 2000 is $314. The y-intercept should not be interpreted.
Use the least squares regression line of this data set to predict a value. 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. The least squares regression line of this data set is: y = 8.116x + 273.273 How much rainfall does this line predict in a year if the average temperature of coastal waters is 15 degrees Celsius? Round your answer to the nearest integer. millimetres
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…
A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). Σx = 90 Σ(y - )(x - ) = 466 Σy = 170 Σ(x - )2 = 234 n = 10 Σ(y - )2 = 1434 SSE = 505.98 The least squares estimate of the slope or b1 equals a. .923. b. 1.991. c. -1.991. d. -.923.
A study was conducted to assess the relationship between students’s score in final exam (y) and number of hours spent for exam (x) in each day. Data on a random sample 20 students were obtained and a regression model was estimated; and the least squares estimates obtained are: intercept a=28.5 and slope b=4.3 with SE(b)=Sb=0.017. The SS are: TSS=2540 and ESS=850. ****** QA) What is the difference between exam score obtained by two students one who studied 5 hours and the other who studied 9 hours per day. QB) In the above Question 1, find 95% CI for the slope and interpret it. In the above Question 1, find and interpret the coefficient of determination (r-square value).