Concept explainers
The authors of the paper “Weight-Bearing Activity during Youth Is a More Important Factor for Peak Bone Mass than Calcium Intake” (Journal of Bone and Mineral Density [1994]: 1089–1096) used a multiple regression model to describe the relationship between
- a. The authors concluded that both body weight and weight-bearing activity were important predictors of bone mineral density and that there was no significant interaction between body weight and weight-bearing activity. What multiple regression
function is consistent with this description? - b. The value of the coefficient of body weight in the multiple regression function given in the paper is 0.587. Interpret this value.
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Chapter 14 Solutions
Introduction To Statistics And Data Analysis
- 1a) Use the F statistic to test the significance of the relationship at a 0.05 level of significance. 1b)How many apartment buildings were in the sample? 1c)Predict the selling price (in thousands of dollars) of an apartment building with gross annual rents of $30,000.arrow_forwardAnkitarrow_forwardA researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.3 14.9x Coefficients (Intercept) X Estimate St 4.3 Ho: B₁ = 0 Ha: B₁ > 0 B1 O Ho: B₁ Ha: B₁ <0 = 0 14.9 B1 O Ho: B₁ = 0 0 Ha: B1 Std. Error Test statistic P-value 2.9 5.1 1.48 Specify the null and the alternative hypotheses that you would use in order to test whether a negative linear relationship exists between x and y. 2.92 0.08 0.01arrow_forward
- Friesen and Shine (2019) wanted to determine whether male Australian cane toads have different testes sizes in different parts of the species' range (edge of the range vs. core of the range). As part of the study, they needed to quantify how big a toad's testes are relative to the toad's body size. They decided to perform a linear regression of total testes mass (in mg) against body mass (in g) and use the residual for each toad as a measure of the toad's relative testes size. The Coefficient Estimates table for their least-squares regression procedure is shown below. Term Coefficient Standard Error t-value Pr > |t| (Intercept) 19.192 43.082 0.44547 0.65643 body mass 3.0063 0.36387 8.262 1.5733e-1 (a) Suppose the researchers do a t-test for the slope of the linear model. Write the null hypothesis for the test and show that, under the null hypothesis, the observed value of the t-statistic is indeed 8.262. (That is, do the appropriate computations to prove the value is 8.262) (b) The…arrow_forwardA researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.5+ 14.4x Coefficients (Intercept) x Estimate 4.5 Ho: B₁ = 0 H₁: B₁ > 0 Ho: B₁ = 0 Ha: B₁ <0 14.4 Ho: B₁ = 0 Ha: B₁ #0 Std. Error Test statistic 2.9 4.7 1.55 3.06 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a linear relationship exists between x and y. 0.07 0arrow_forwardAcrylamide is a chemical that is sometimes found in cooked starchy foods and which is thought to increase the risk of certain kinds of cancer. The paper "A Statistical Regression Model for the Estimation of Acrylamide Concentrations in French Fries for Excess Lifetime Cancer Risk Assessment"t describes a study to investigate the effect of x = y = acrylamide concentration (in micrograms per kg) in French fries. The data in the accompanying table are approximate values read from a graph that appeared in the paper. frying time (in seconds) and %3D Frying Time Acrylamide Concentration 150 155 240 115 240 190 270 180 300 140 300 265arrow_forward
- A study of the effect of massage on boxing performance measured a boxer's blood lactate concentration (in mM) and perceived recovery (on a 28-point scale). On the basis of the information provided by the study, the data shown in the accompanying table were obtained for 16 five-round boxing performances in which a massage was given to the boxer between rounds. Conduct a test to determine whether blood lactate level (y) is linearly related to perceived recovery (x). Use α = 0.10. Click the icon to view the table of boxer blood data. X Boxer Blood Data Perceived Recovery Determine the correct null and alternative hypotheses. Choose the correct answer below. Blood Lactate Level 3.8 4.4 8 8 O A. Ho: B₁ 0 OB. Ho: B₁0, H₂: B₁ 0 4.1 11 5.0 11 = E. Ho: B₁0, H₂: B₁ #0 OF. Ho: B₁ #0, H₂: B₁ = 0 1 a 1 5.3 11 4.2 14 Find the test statistic. 2.4 17 t = (Round to three decimal places as needed.) 3.7 17 5.3 17 5.8 18 6.0 18 5.9 21 6.3 21 5.5 20 6.5 27arrow_forwardA. Do these data provide sufficient evidence that there is a positive linear relationship between the two variables? B. What does R^2 imply? C. Using the regression model, predict the blood pressure level associated with a sound pressure of 7.5 decibels.arrow_forwarda, b, and carrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning