The following data were obtained in a study of depth (x, measured in meters), ve

Question

The following data were obtained in a study of depth (x, measured in meters), versus temperature (y, measured in degree C) above the thermocline layer in the Mediterranean Sea. (a) Using your calculator, find the equation for the line of best fit for this data and state it. (b At a depth of 85 meters, what is your prediction for the water temperature? (c) What percentage of the variability in the water temperature can be explained by the regression line? (d) Conduct a two-sided t-test (concerning beta_1) for a significant regression. Use a significant level of 0.05. State your conclusion using a sentence.

Explanation / Answer

following information has been generated using the given data

(a) y=23.09173-0.08395x

(b)for x=85, y=23.09173-0.08395*85=15.96

(c) here R2=0.5817 so% of variability explained by regression line=58.17

(d) P-value of t-test of regression coefficeint is 0.0277 which is less than level of significance alpha=0.05,

so regression coefficient is significant.

t=coefficient/SE(coefficient)=-0.08395/0.02906=-2.89 and its two tailed P-value=0.0277

Analysis of Variance Source DF Sum of Mean F Value P-value Squares Square Model 1 108.5448 108.545 8.34 0.0277 Error 6 78.05517 13.0092 Corrected Total 7 186.6 Root MSE 3.60683 R-Square 0.5817 Dependent Mean 15.2 Adj R-Sq 0.512 Coeff Var 23.7291 Parameter Estimates Variable DF Parameter Standard t Value P-value Estimate Error Intercept 1 23.09173 3.01503 7.66 0.0003 x 1 -0.08395 0.02906 -2.89 0.0277

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