A statistical program is recommended.Electromagnetic technologies offer effective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the material depends on its dielectric properties. The following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures andRelationship with Density,"t was used to relate y = dielectric constant to x = air void (%) for 18 samples having 5% asphalt content.y 4.55 4.49 4.50 4.47 4.47 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.33 4.44 4.40 4.26 4.32 4.34x 4.35 4.79 5.57 5.20 5.07 5.79 5.36 6.40 5.66 5.90 6.49 5.70 6.49 6.37 6.51 7.88 6.74 7.08The following R output is fromsimple linear regression of y on x.EstimateStd. Errort valuePr (>|t|)(Intercept)4.8586910.05976881.283<2e-16AirVoid-0.0746760.009923-7.5261.21e-06Residual standard error: 0.03551 on 16 DF MultipleR-squared: 0.7797,F-statistic: 56.63 on 1 and 16 DF,Adjusted R-squared: 0.766p-value: 1.214e-06Analysis of Variance TableResponse: DielectricDfSum SqMean SqF valuePr (>F)Airvoid1.0.0714220.07142256.6351.214e-06Residuals160.201780.001261(a) Obtain the equation of the least squares line. (Enter your numerical values to six decimal places.)Interpret the slope of the equation of the least squares line.According to the slope, a one-percentage-point increase in air void is associated with an estimated --Select--- V in dielectric constant of ---Select---(b) What percentage of observed variation in dielectric constant can be attributed to the approximate linear relationship between dielectric constant and air void? (Round your answer to two decimal places.)%(c) Does there appear to be a useful linear relationship between dielectric constant and air void? Carry out a test of appropriate hypotheses using a significance level of 0.01.State the appropriate null and alternative hypotheses.O Ho: B, = 0H: B, < 0O Ho: B1 = 0H: B * 0O Ho: B1 +0H: B2 = 0O Họ: B = 0Hi B1 > 0Find the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)t =P-value =

The independent variable is air void. The dependent variable is dielectric constant. This is simple…

Electromagnetic technologies offer affective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the material depends on its dielectric properties. The following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures and Relationship with Density," was used to relate y dielectric constant to xair void (%) for 18 samples having 5% asphalt content. y 4.55 4.49 4.50 4.47 4.47 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.33 4.44 4.40 4.26 4.32 4.34 * 4.35 4.79 5.57 5.20 5.07 5.79 5.36 6.40 5.66 5.90 6.49 5.70 6.49 6.37 6.51 7.88 6.74 7.08 The following R output is from a simple linear regression of y on x. Estimate 4.050691 -0.074676 t value Pr (>It|) <2e-16 Std. Error (Intercept) 0.059768 81.203 AirVoid 0.009923 824.ר- 1.21e-06 Residual standard error: 0.03551 on 16 DF Muitiple R-aquaredi 0.7797, Adjusted R-squared: 0.766 F-statistie: 56.63 on 1 and 16 DF, p-value: 1.214e-06 Analysis of Variance Table Response: Dielectrie P value 56.635 DE Sum Sq 0.071422 Mean Sq Pr (>P) Airvoid Residuale 16 0.071422 1.214e-06 0.20178 0.001261 (a) Obtain the equation of the least squares line. (Enter yeur numerical values to six decimal places.) Interpret the slope of the equation of the least squares line. According to the slope, a one-percentage-point increase in air void is associated with an estimated elect v in dielectric constant of eect v. (b) What percentage of observed variation in dielectric constant can be attributed to the approximate linear relationship betwreen dielectric constant and air void? (Round your answer to two decimal places.) (e) Does there appear to be a useful linear relationship between dielectric constant and air void? Carry out a test of appropriate hypotheses using a significance level of 0.01. State the appropriate null and alternative hypotheses. O Hai -0 Find the test statistic value and find the Pvalue. (Round your test statistic to two decimal places and your Pvalue to three decimal places.) Pvalue

Electromagnetic technologies offer affective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the material depends on its dielectric properties. The following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures and Relationship with Density," was used to relate y dielectric constant to xair void (%) for 18 samples having 5% asphalt content. y 4.55 4.49 4.50 4.47 4.47 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.33 4.44 4.40 4.26 4.32 4.34 * 4.35 4.79 5.57 5.20 5.07 5.79 5.36 6.40 5.66 5.90 6.49 5.70 6.49 6.37 6.51 7.88 6.74 7.08 The following R output is from a simple linear regression of y on x. Estimate 4.050691 -0.074676 t value Pr (>It|) <2e-16 Std. Error (Intercept) 0.059768 81.203 AirVoid 0.009923 824.ר- 1.21e-06 Residual standard error: 0.03551 on 16 DF Muitiple R-aquaredi 0.7797, Adjusted R-squared: 0.766 F-statistie: 56.63 on 1 and 16 DF, p-value: 1.214e-06 Analysis of Variance Table Response: Dielectrie P value 56.635 DE Sum Sq 0.071422 Mean Sq Pr (>P) Airvoid Residuale 16 0.071422 1.214e-06 0.20178 0.001261 (a) Obtain the equation of the least squares line. (Enter yeur numerical values to six decimal places.) Interpret the slope of the equation of the least squares line. According to the slope, a one-percentage-point increase in air void is associated with an estimated elect v in dielectric constant of eect v. (b) What percentage of observed variation in dielectric constant can be attributed to the approximate linear relationship betwreen dielectric constant and air void? (Round your answer to two decimal places.) (e) Does there appear to be a useful linear relationship between dielectric constant and air void? Carry out a test of appropriate hypotheses using a significance level of 0.01. State the appropriate null and alternative hypotheses. O Hai -0 Find the test statistic value and find the Pvalue. (Round your test statistic to two decimal places and your Pvalue to three decimal places.) Pvalue

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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