Concept explainers
The ability of ecologists to identify regions of greatest species richness could have an impact on the preservation of genetic diversity, a major objective of the World Conservation Strategy. The article “Prediction of Rarities from Habitat Variables: Coastal Plain Plants on Nova Scotian Lakeshores” (Ecology [1992]: 1852–1859) used a sample n = 37 lakes to obtain the estimated regression equation
where y = Species richness, x1 = Watershed area, x2 = Shore width, x3 = Drainage (%), x4 = Water color (total color units), x5 = Sand (%), and x6 = Alkalinity. The coefficient of multiple determination was reported as R2 = 0.83. Use a test with significance level 0.01 to decide whether the chosen model is useful.
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Chapter 14 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_forwardOlympic 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?arrow_forward
- A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+????Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained:Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%Analysis of VarianceSource DF SS MS F pRegression 3 1991.31 663.77 ? ??Error 12 77.4 6.45Total 15 Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq” and comment on its value.arrow_forwardA) Compute the last-squares regression line for predicting US emission from NON US - emissions. b) If the non-US emission differ by 0.2 from one year to the next by how much would you predict the US- emission to differ?arrow_forwardWe have data on Lung Capacity of persons and we wish to build a multiple linear regression model that predicts Lung Capacity based on the predictors Age and Smoking Status. Age is a numeric variable whereas Smoke is a categorical variable (0 if non-smoker, 1 if smoker). Here is the partial result from STATISTICA. b* Std.Err. of b* Std.Err. N=725 of b Intercept Age Smoke 0.835543 -0.075120 1.085725 0.555396 0.182989 0.014378 0.021631 0.021631 -0.648588 0.186761 Which of the following statements is absolutely false? A. The expected lung capacity of a smoker is expected to be 0.648588 lower than that of a non-smoker. B. The predictor variables Age and Smoker both contribute significantly to the model. C. For every one year that a person gets older, the lung capacity is expected to increase by 0.555396 units, holding smoker status constant. D. For every one unit increase in smoker status, lung capacity is expected to decrease by 0.648588 units, holding age constant.arrow_forward
- The model developed from sample data that has the form of Yhat = bo +bjX is known as the multiple regression model with two predictor variables. (True or False) O True O Falsearrow_forwardA researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+???I Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 Oil 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 * 0.0057 FDI -396.99 160.66 -2.471 ** S = 2.45 R – sq = 96.3% R – sq (adj) = 95.3% Analysis of Variance Source DF SS MS F P Regression 3 1991.31 663.77 ? ?? Error 12 77.4 6.45 Total 15 e) Perform the F Test making sure to state…arrow_forward13) Use computer software to find the multiple regression equation. Can the equation be used for prediction? An anti-smoking group used data in the table to relate the carbon monoxide( CO) of various brands of cigarettes to their tar and nicotine (NIC) content. 13). CO TAR NIC 15 1.2 16 15 1.2 16 17 1.0 16 6. 0.8 1 0.1 1 8. 0.8 8. 10 0.8 10 17 1.0 16 15 1.2 15 11 0.7 9. 18 1.4 18 16 1.0 15 10 0.8 9. 0.5 18 1.1 16 A) CO = 1.37 + 5.50TAR – 1.38NIC; Yes, because the P-value is high. B) CÓ = 1.37 - 5.53TAR + 1.33NIC; Yes, because the R2 is high. C) CO = 1.25 + 1.55TAR – 5.79NIC; Yes, because the P-value is too low. D) CO = 1.3 + 5.5TAR - 1.3NIC; Yes, because the adjusted R2 is high. %3Darrow_forward
- A researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+???? Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 * 0.0057 FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%…arrow_forwardA researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+???? Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 -3.3611 0.0057 FDI -396.99 160.66 -2.471 0.0000 S =2.45 R-sq = 96.3% R-sq (adj) = 95.3% Analysis of Variance Source DF…arrow_forwardA researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+???? Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 -3.361 0.0057 FDI -396.99 160.66 -2.471 ** S =2.45 R-sq = 96.3% R-sq (adj) = 95.3% (a) Fill in the missing values ‘**’, and ‘??’ (b) Hence test…arrow_forward
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