What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size o the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Coefficient Constant Size Std Error T P -2298.36 158.531 -14.50 0.0000 11598.9 230.111 50.41 0.0000 R-Squared Adjusted R-Squared 0.8925 Resid. Mean Square (MSE) 1248950 0.8922 Standard Deviation 1117.56 Interpret the coefficient of determination for the regression model. A) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values. B) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56. C) There is sufficient evidence to indicate that the size of the diamond is a useful predictor of the price of a diamond when testing at alpha = 0.05. D) We can explain 89.25% of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model.

What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size o the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Coefficient Constant Size Std Error T P -2298.36 158.531 -14.50 0.0000 11598.9 230.111 50.41 0.0000 R-Squared Adjusted R-Squared 0.8925 Resid. Mean Square (MSE) 1248950 0.8922 Standard Deviation 1117.56 Interpret the coefficient of determination for the regression model. A) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values. B) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56. C) There is sufficient evidence to indicate that the size of the diamond is a useful predictor of the price of a diamond when testing at alpha = 0.05. D) We can explain 89.25% of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 76E

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