Question 1
The average sea surface temperature (in degree Celsius) and thecoral growth (in millimetres per year) over 18 years at aparticular location are observed. An excerpt of the data is shownin the table below:
Temperature (x)= 29.61 29.82 30.25 … 30.96
Growth (y)= 2.63 2.58 2.49 … 2.26
The output from R Commander appears on the next page
(c) Using the R Commander output, calculate the correlationcoefficient between the two variables. [2 marks]
(d) Test the significance of the slope of the linear regressionline at the 5% level of significance. State clearly the null andalternative hypotheses, the name of the test or the test statistic,decision rule, test result and conclusion in terms of the originalproblem. [6 marks]
(e) Write down the linear regression equation for the data.(1MARK)
(f) Interpret the slope of the linear regression equation. [1mark]
(g) Use the equation in (e), predict the coral growth when theaverage sea surface temperature is 30 degree Celsius. [1 mark]
(h) Comment on the appropriateness of the prediction in (g). [2marks]
(i) Write down three assumptions underlying the analysis. [3marks]
> summary(RegModel.1)
Call: lm(formula = Growth ~ Temperature, data = Q1)
Residuals:
Min 1Q Median 3Q Max
-0.10279 -0.04107 -0.01688 0.04901 0.09864
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.81986 1.11135 7.036 2.81e-06 ***
Temperature -0.17860 0.03698 -4.830 0.000185 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' '1
Residual standard error: 0.06155 on 16 degrees of freedom
Multiple R-squared: 0.5931, Adjusted R-squared: 0.5677
F-statistic: 23.33 on 1 and 16 DF, p-value: 0.0001848
