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.
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- 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_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
- 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_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
- Infant Mortality Rates. In the article “Children’s Environmental Index,” the ZPG (September, 1997) provided data for 219 U.S. cities on 20 variables that measure aspects of the quality of life for children. In this exercise, we consider the relationship between infant mortality rate (1990–1994) and the following 11 predictor variables. 1. Density (population per square mile) 2. Birth rate per 1000 population (1988) 3. Percentage of births to teens (1994) 4. Physicians per 1000 population (1995) 5. Student-to-teacher ratio in schools (1993–1994) 6. Student drop-out rate (1990) 7. Unemployment rate (1995) 8. Percentage of children in poverty (1989) 9. Violent crimes per 1000 population (1995) 10. Percentage of juvenile arrests (1995) 11. Pounds of toxic releases per 1000 population (1994) We will use the data in the table on pages B-145–B-147, obtained from the article, for 50 cities chosen randomly from the 219 cities considered. Use the technology of your choice to do the following. a.…arrow_forwardThe local utility company surveys 11 randomly selected customers. For each survey participant, the company collects the following: annual electric bill (in dollars) and home size (in square feet). Output from a regression analysis appears below: Bill = 12.4 +4.54*Size Coefficients Estimate Std. Error (Intercept) 12.4 Size 4.54 0.6 0.85 dollars and We are 80% confident that the mean annual electric bill increases by between dollars for every additional square foot in home size. Round your answers to three decimal places and enter in increasing order.arrow_forward9(20 pts). Correlation analysis and Simple Linear Regression. A study is con- ducted with a group of dieters to see if the number of grams of fat each consumes per day, x, is related to cholesterol level y. The data are shown in Spreadsheet "Question 8": Fat Grams x: 6.8 5.5 8.2 10 8.6 9.1 8.6 10.4 5.9 6.3 7.6 8 8.5 7.9 5.9 6.7 9.1 10.1 9.5 8.9 Cholesterol Level y: 212 192 193 263 222 250 190 249 190 185 192 201 215 189 203 194 241 256 255 245 pole sta ber of of perm lity o n = 20, Στ = 161.6, y = 216.85, Σ Υ = 4337, = 8.08, Σν = 955159. Στ? = 1347.52, Σ y = 35671.5, (a) Compute the value of the correlation coefficient, r, between x and y. (b) Test if the population correlation coefficient p > 0.5 at a = 0.05. (c) Determine the regression line equation y' = a + bx. (d) Predict the cholesterol level of a dieter who consumes x = 8.5 grams of fat per day. (e) Find the 90% prediction interval of the cholesterol level of a person who consumes x=8.5 grams of fat per day. at mo 9 mally tribu…arrow_forward
- A paper described a study that examined whether stress accelerates aging at a cellular level. The accompanying data on a measure of perceived stress (x) and telomere length (y) were read from a scatterplot that appeared in the paper. Telomere length is a measure of cell longevity. Perceivedstress Telomerelength Perceivedstress Telomerelength 5 0.93 20 1.19 6 0.94 20 0.95 6 0.96 20 0.91 7 0.92 21 0.95 10 1.14 21 1.2 11 1.03 21 1.08 12 0.92 22 1.11 13 1.06 22 1.23 14 0.99 22 0.89 14 0.9 23 1.27 15 1.16 24 0.94 15 1.07 24 1.08 15 1.09 25 1.2 17 0.95 26 0.98 17 0.93 27 1.16 17 1.11 27 1.25 18 1.01 28 1 18 1.07 29 1.22 19 1.15 33 0.9 (a) Compute the equation of the least-squares line. (Round your answer to four decimal places.)y = (b) What is the value of r2? (Round your answer to four decimal places.)r2 =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). Altitude Temperature a. Find the explained variation. 2 55 8 40 10370.30 (Round to two decimal places as needed.) b. Find the unexplained variation. 53.70845 (Round to five decimal places as needed.) c. Find the indicated prediction interval. °Farrow_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). Altitude Temperature 2 55 a. Find the explained variation. 8 40 10370.30 (Round to two decimal places as needed.) b. Find the unexplained variation. (Round to five decimal places as needed.) 13 25 20 - 3 28 - 26 31 41 34 - 53arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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