Consider the following data for two variables, x and y. 32 18 15 9 26 y 10 21 | 22 17| 23 (a) Develop an estimated regression equation for the data of the form ý = b, + b,x. (Round b, to two decimal places and b, to three decimal places.) Comment on the adequacy of this equation for predicting y. (Use a = 0.05.) O The high p-value and low coefficient of determination indicate that the equation is inadequate. O The high p-value and high coefficient of determination indicate that the equation is adequate. O The low p-value and low coefficient of determination indicate that the equation is inadequate. O The low p-value and high coefficient of determination indicate that the equation is adequate. (b) Develop an estimated regression equation for the data of the form ý = b, + b,x + b,x². (Round b, to two decimal places and b, to three decimal places and b, to four de places.) Comment on the adequacy of this equation for predicting y. (Use a = 0.05.) O The high p-value and low coefficient of determination indicate that the equation is inadequate.

Consider the following data for two variables, x and y. 32 18 15 9 26 y 10 21 | 22 17| 23 (a) Develop an estimated regression equation for the data of the form ý = b, + b,x. (Round b, to two decimal places and b, to three decimal places.) Comment on the adequacy of this equation for predicting y. (Use a = 0.05.) O The high p-value and low coefficient of determination indicate that the equation is inadequate. O The high p-value and high coefficient of determination indicate that the equation is adequate. O The low p-value and low coefficient of determination indicate that the equation is inadequate. O The low p-value and high coefficient of determination indicate that the equation is adequate. (b) Develop an estimated regression equation for the data of the form ý = b, + b,x + b,x². (Round b, to two decimal places and b, to three decimal places and b, to four de places.) Comment on the adequacy of this equation for predicting y. (Use a = 0.05.) O The high p-value and low coefficient of determination indicate that the equation is inadequate.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

See similar textbooks

Similar questions

Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
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?
A researcher conducted a number of descriptive statistics for two variables X and Y. They were as follows: SP = -20; SSx = 4; My = 7; Mx = 3 What is b equal to? What is a equal to? Using b and a construct a regression equation, and then using the regression equation, calculate the value of predicted Y when X = 2?
Consider the following data for two variables, x and y. x 9 32 18 15 26 y 9 19 20 15 22 Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to two decimal places and b1 to three decimal places and b2 to four decimal places.) ŷ = (c) Use the model from part (b) to predict the value of y when x = 20. (Round your answer to two decimal places.)
Given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 7 18 9 26 23 Compute b0 and b1 (to 1 decimal).b1 b0 Complete the estimated regression equation (to 1 decimal).^y = + x Use the estimated regression equation to predict the value of y when x = 6 (to 1 decimal).^y =
Consider a simple linear regression model Y=α+βX+ε. We have collected 15 samples, from which we calculated the summary statistics ∑xi=66, ∑x2i=6568, ∑yi=459, ∑y2i=27933, ∑xiyi=11311. Suppose one of the data is supposed to be (x1=10, y1=30), but is incorrectly recorded as (x1=7, y1=34). All other observations are correctly recorded. What is the OLS estimators αˆ= ? and βˆ= ? based on the correct data.
A study was done that examined the effectiveness of a 7-Minute Screen test for Alzheimer’s disease. The study evaluated the relationship between scores from the 7-Minute Screen and scores for the same patients from a set of cognitive exams that are typically used to test for Alzheimer’s disease. For a sample of n=9 patients, the scores for the 7-Minute Screen averaged M=7 with SS = 92. The cognitive test scores averaged M=17 with SS = 236. For these data, SP = 127. Find the regression equation for predicting the cognitive scores from the 7-Minute Screen score. b = a = Regression equation = What percentage of variance in the cognitive scores is accounted for by the regression equation? r = r2 = Does the regression equation account for a significant portion of te variance in the cognitive scores? Use α = .05 to evaluate the F ratio. MSregression = MSresidual = Fcalculated = Fcritical = Decision =
The following table displays the mathematics test scores for a random sample of college students, along with their final SY16C grades. a. Fit the regression line y = a+bx to the data and interpret the results. b. Use the regression equation to determine the SY16C grade for a college student who scored60 on their achievement test. What would their SY16C grade be?
An investigation into the relationship between an adolescent mother's age x in years and the birth weight y of her baby in grams yielded the regression equation y= - 1163.45 + 245.15x as well as r = .88369, r2= .78091, SSE = 337212.45, and s= 205.30844 1) What is the predicted birth weight for a baby brn to a 17 year old woman? 2) What is the propotion of the variability in the weights of babies born to adolescent mothers that is accounted for by the mother's age? 3) For every additional year in the mother's age that mean birth weight of the baby? (a) increases by about 245g (b) decreases by about 245g (c) increases by about 1163g (d) increases by about 1163g (e) changes by an amount that cannot be determined from the information given.
The grades of a sample of 9 students on a prelim exam (x) and on the midterm exam (y) are shown below. Find the regression equation. y = 34.661 + 0.433x y = 0.777 + 12.0623x y = 12.0623 + 0.777x y = 34.661 - 0.433x
We wish to estimate the effect of weight on serum cholesterol (S. C.) level in healthy females aged between 20 and 25. To estimate the regression equation of S.C. level on weight, a random sample of 10 females in this age class was taken, with the following results: a. Compute (beta) B^ 1 the estimate of the slope coefficient b. Compute (beta) B^ 0 the estimate of the intercept person# 1 2 3 4 5 6 7 8 9 10 X 53.7 56.8 54.1 54.4 55.1 55.8 56.3 57.1 56.6 57.6 Y 124.8 126.2 125.7 125.1 126.5 124.6 126.4 127.8 127.3 127.4