Find the equation of the least squares regression lineof y on x, for the following sets of data:(a)3489.11 144 5 78.y1249

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
The least-squares regression line relating two statistical variables is given as = 24 + 5x. Compute the residual if the actual (observed) value for y is 38 when x is 2. 4 38 2
Compute the least-squares regression line for predicting y from x given the following summary statistics. Round the slope and y -intercept to at least four decimal places. =x8.2 =sx3 =y1350 =sy13,000 =r0.40
Compute the least-squares regression equation for the given data set. Use a TI-84 calculator. Round the slope and y-Intercept to at least four decimal places.
For the regression model Yi = b0 + eI, derive the least squares estimator.
Given are five observations for two variables, x and y. xi 3 8 12 18 20 yi 54 57 50 24 11 -select your answer choices- b. The least squares line provided an (good, bad) fit; __ % of the variability in y has been explained by the estimated regression equation (to 1 decimal)
Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?
Compute the least-squares regression equation for the given data set. Round the slope and y-intercept to at least four decimal places. 2 4 7 6 6 5 3 3 4 2
What is the least squares regression line for the following scatter plot? y-hat = 0.89x + 1.36 y-hat = 0.31x + 1.95 y-hat = 0.67x + 0.87 y-hat = 1.05x + 1.37
Given the estimated least square regression line y=2.48+1.63x, and the coefficient of determination of 0.81, What is the value of correlation coefficient?
Consider the following correlations -0.9 , -0.5 , -0.2 , 0 , 0.2 , 0.5 and 0.9. For each give the fraction of the variation in y that is explained by the least-squares regression of y on x.
Given below are five observations collected in a regression study on two variables, x(independent variable) y, ( dependent variable). x y 11 8 21 41 31 5 51 2 Develope the least squares estimated regression equation Compute the coefficient of determination and the coefficient of correlation

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Find the equation of the least squares regression line of y on x, for the following sets of data: (a) X 1 3 4 6 8 9 11 14 9 y 1 2 44578