Match the following definitions with the correct terms. Dat involving two variables. Bivariate Data Estimation of a model output using an input [ Choose ] outside of the data set. A regression that minimizes the total sum of Linear Regression errors-squared A plot in which the y data is transformed to [ Choose ] In(y) Fitting a linear model to bivariate data. V[ Choose ] Quadratic Regression Log-log Plot Linear Regression Interpolation Bivariate Data

Match the following definitions with the correct terms. Dat involving two variables. Bivariate Data Estimation of a model output using an input [ Choose ] outside of the data set. A regression that minimizes the total sum of Linear Regression errors-squared A plot in which the y data is transformed to [ Choose ] In(y) Fitting a linear model to bivariate data. V[ Choose ] Quadratic Regression Log-log Plot Linear Regression Interpolation Bivariate Data

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...

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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?
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 4
Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2
In this regression, which test statistic would you use to test the nullhypothesis that the regression function is linear against the alternativethat it is cubic? If the value of that statistic is 37.7 with associatedp-value 0.0001, what would your conclusion be?
For a multiple regression model involving 46 observations, the following estimated regression equation was obtained. ^y = 17 + 4x1 - 3x2 + 8x3 + 5x4 + 8x5 For this model, SST = 3410 and SSE = 510. Compute the multiple coefficient of determination. Perform an F test and determine whether or not the regression model is significant. Use level of significance as 5%.
Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual salary in dollars of an employee with 5 years of experience and a bachelor’s degree?
Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual starting salary of an employee with a doctorate degree? (Someone with no work experience). $ What is the predicted bi-annual starting salary of an employee with a bachelor’s degree? (Someone with no work experience). $
In a regression analysis involving 25 observations, the following estimated regression equation was developed.ŷ = 10 – 18x1 + 3x2 + 14x3Also, the following standard errors and the sum of squares were obtained.Sb1 = 3 Sb1 = 6 Sb1 = 7SST = 4,800 SSE = 1,296If we are interested in testing for the significance of the relationship among the variables (i.e., significance of the model), the critical value of F at α = .05 is _____.
Which of the following does not need to be computed to determine a simple regression line? SSx SP "Y-hat" SSy
If a set of paired data gives the indication that the regression equation is of the form μY|x = α · βx, it is cus-tomary to estimate α and β by fitting the line log ˆy = log ˆα + x · log βˆ to the points {(xi, log yi);i = 1, 2, ... , n} by the methodof least squares. Use this technique to fit an exponentialcurve of the form ˆy = αˆ · βˆx to the following data on thegrowth of cactus grafts under controlled environmentalconditions: Weeks after Heightgrafting (inches)x y1 2.02 2.44 5.15 7.36 9.48 18.3
A student used multiple regression analysis to study how family spending (y) is influenced by income(x1), family size (x2), and addition to savings(x3). The variables y, x1, and x3 are measured in thousandsof dollars. The following results were obtained.ANOVAdf SSRegression 3 45.9634Residual 11 2.6218TotalCoefficients Standard ErrorIntercept 0.0136x10.7992 0.074x20.2280 0.190x3-0.5796 0.920a. Write out the estimated regression equation for the relationship between the variables. b. Compute the coefficient of determination. What can you say about the strength of thisrelationship? c. Carry out a test to determine whether y is significantly related to the independent variables.Use a 5% level of significance. d. Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.