Concept explainers
The following quote is from the paper “Evaluation of the Accuracy of Different Methods Used to Estimate Weights in the Pediatric Population” (Pediatrics [2009]: e1045–e1051):
As expected, the model demonstrated that weight increased with age, but visual inspection of an age versus weight plot demonstrated a nonlinear relationship unless infants and children were analyzed separately. The linear coefficient for age as a predictor of weight was 6.93 in infants and 3.1 to 3.48 in children.
This quote suggests that when a
Briefly explain why the relationship between weight and age in the scatterplot for the combined group would appear nonlinear.
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Introduction to Statistics and Data Analysis
- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardA regression model to predict Y, the state burglary rate per 100,000 people, used the following four state predictors: X₁ = median age, X₂ = number of bankruptcies per 1.000 population, X3 = federal expenditures per capita (a leading predictor), and X4 = high school graduation percentage. Click here for the Excel Data File (a) Using the sample size of 50 people, calculate the calc and p-value in the table given below. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.) Predictor Intercept AgeMed Bankrupt FedSpend HSGrad% Answer is complete but not entirely correct. *calc 5.2526 -2.1764✔✔ 1.4101✔ Coefficient 4,198.5808 -27.3540 17.4893 -0.0124 -29.0314 SE 799.3395 12.5687 12.4033 0.0176 7.1268 -0.7045 -4.0736 p-value 0.0000 0.0348 0.2935 0.4848 0.0002arrow_forward
- The administration of a midwestern university commissioned a salary equity study to help establish benchmarks for faculty salaries. The administration utilized the following regression model for annual salary, y : ?(?) β0+β1x ,where ?=0 if lecturer, 1 if assistant professor, 2 if associate professor, and 3 if full professor. The administration wanted to use the model to compare the mean salaries of professors in the different ranks. a) Explain the flaw in the model. b)Propose an alternative model that will achieve the administration’s objective. c) If the global F-test for the model you proposed in 2 is conducted, what would be the value of the numerator degrees of freedom?arrow_forwardWhich non-parametric test for ordinal data is the best to use in the given scenario? In a study by Zuckerman and Heneghan, hemodynamic stresses were measured on subjects undergoing laparoscopic cholecystectomy. An outcome variable of interest was the ventricular end-diastolic volume (LVEDV) measured in mm. A portion of the data appears in the following table. Baseline refers to a measurement taken 5 minutes after induction of anesthesia, and the term '5 minutes' refers to a measurement taken 5 minutes after baseline. Can we conclude that, on the basis of these data, among subjects undergoing laparoscopic cholecystectomy, the average LVEDV levels change? Let a =.01. LVEDV (ml) Subject Baseline 5 minutes 1 51.7 49.3 2 79.0 72.0 3 78.7 67.0 4 80.3 70.4 5 72.0 65.9 6 85.0 84.8 7 79.0 77.7 8 71.3 74.0 9 54.3 58.0 10 58.8 65.0 a. Mood Median Test b. Sign Test c. Wilcoxon Rank Sum Test d. Wilcoxon Matched-Pair Signed-Ranks Test e. Spearman and Kendall Correlation…arrow_forwardListed below are altitudes (thousands of feet) and outside air temperatures ("F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet). 32 -53 8 16 22 21 29 -27 Altitude 31 Temperature 60 40 -41 a. Find the explained variation. (Round to two decimal places as needed.)arrow_forward
- A regression model to predict Y, the state burglary rate per 100,000 people, used the following four state predictors: X1 = median age, X2 = number of bankruptcies per 1,000 population, X3 = federal expenditures per capita (a leading predictor), and X4 = high school graduation percentage. Click here for the Excel Data File (a) Using the sample size of 45 people, calculate the tcalc and p-value in the table given below. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p- values to 4 decimal places.) Predictor Intercept AgeMed Coefficient SE tcalc p-value 4,641.0430 798.0634 -28.8630 12.4684 Bankrupt 20.1604 12.1079 FedSpend HSGrad% -0.0181 0.0181 -30.3196 7.1136 (b-1) What is the critical value of Student's tin Appendix D for a two-tailed test at a = .01? (Round your answer to 3 decimal places.) -value =arrow_forwardConsider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables? (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly. (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly. (d) Suppose a second regression model (Model 2) was generated using only…arrow_forwardConsider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables? (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly. (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly. (d) Suppose a second regression model (Model 2) was generated using only…arrow_forward
- Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables? (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly. (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly. (d) Suppose a second regression model (Model 2) was generated using only…arrow_forwardA regression model to predict Y, the state burglary rate per 100,000 people, used the following four state predictors: X₁ = median age, X₂ = number of bankruptcies per 1,000 population, X3 = federal expenditures per capita (a leading predictor), and X4 = high school graduation percentage. Click here for the Excel Data File (a) Using the sample size of 50 people, calculate the tcalc and p-value in the table given below. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.) Predictor Intercept AgeMed Bankrupt FedSpend HSGrad% Coefficient t-value = 4,198.5808 -27.3540 17.4893 -0.0124 -29.0314 SE 799.3395 12.5687 12.4033 0.0176 7.1268 tcalc p-value (b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at a = .01? (Round your answer to 3 decimal places.)arrow_forward2)arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt