In this exercise, we will investigate the relationship between depth and moistur

Question

In this exercise, we will investigate the relationship between depth and moisture contents of samples from two cores through recent marine muds accumulating in a small inlet on the Gulf Coast in eastern Louisiana. Here is the data (note there are n = 16 observations): Fit the following three models to the data: m_i = beta_0 + beta_1 d_i + ee_i m_i = beta_0 + beta_1 d_i + beta_2 d^2_i + e_i m_i = beta_0 + beta_1 d_i + beta_2 d^2_i + beta_3 d^3_i + e_i It may help to recognize models 2 and 3 as linear models if you let w = d^and v = d^3). Turn in the following information for each model, with each item clearly and unambiguously identified: a. Regression coefficients (i.e., beta_0, beta_1, etc.) b. SSCT c. SSR d. SSE e. MSE. f. s_y, x (the squareroot of MSE) g. r^2 h. T-values for significance of each regression coefficient in each model and conclusion.

Explanation / Answer

Model 1 fits the data.

Regression Statistics Multiple R 0.870418 R Square 0.757627 Adjusted R Square 0.740315 Standard Error 19.23132 Observations 16 ANOVA df SS MS F Significance F Regression 1 16185.19 16185.19 43.76226 1.16E-05 Residual 14 5177.81 369.8435 Total 15 21363 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 98.33333 8.777855 11.20243 2.25E-08 79.50671 117.16 79.50671 117.16 d -2.77619 0.419662 -6.61531 1.16E-05 -3.67628 -1.87611 -3.67628 -1.87611

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