Question

4. Linear Regression [TOTAL 5 MARKS] McDonald (1989) collected the amphipod crustacean Platorchestia platensis on a beach near Stony Brook, Long Island. He removed and counted the number of eggs for 28 females, and then freeze-dried and weighed the mothers (in mg) summary (1m (eggs~mass, eggdata) ) Call 1m (formula data eggdata) eggs mass, Coefficients: Estimate Std. Error t value Pr (>I t|) 12.6890 4.2009 3.021 0.0056 (Intercept) 1.6017 0.6176 2.593 0.0154 mass Signif. codes: 0* 0.001 0.01 0.05 .0.1 '1 Residual standard error: 3.736 on 26 degrees of freedom Multiple R-squared: 0.2055, Adjusted R-squared: 0.175 F-statistic: 6.726 on 1 and 26 DF, p-value: 0.0154 Using this output, answer the following questions () What is the explanatory variable? (ii) What is the response variable? (ii What fraction of the variance in the response variable is accounted for by the explanatory variable? (iv) What is the slope of the relationship between the two variables? ) What null hypothesis is being tested in the second row of t and Prvalues in the output above? (vi) Calculate a 95% confidence interval for the slope of the relationship. Make sure to include all of your workings, including the degrees of freedom you used. (vii) Using the model, estimate the number of eggs for a female of 6 mg.

Answer 1

Solution from tlhe guen date Here, Explanatay vaiable Explanaloy vasiale Cindependlent vaswable) is Hu mothers Cin ma) Response Variable Responx Vasiable (Dependant Vasialle) is Multiple R Sauare the number = 0.2055 :. 20-55 or by explanatory variable fu) The slepe Hhe selationshp betuen the tuwo vaiables variance vin 9tespon& vasuialole is aaunted 1-6017 (It the Coelfreient f mars in tle regrewen explained as: for tach unit incuase in mas average, Syrmbol B1) Slope ealuatien, Lelich is number eags inceares loy 1.G017 On an being lesteol in the Secend sow The nutl hypothesis tand Pr value- is ypobes's is The Ho: B1- D slope That is Test Stat'sbic, t- 2.593

P value O154 at Signhcant Pvalue 0.05, the Hesult is hy petar 5. Jeuel of Signitrcante, aject tle nult wle Vi) a5 Controlen le interual B1+ to for lope x SE CB1) tor 95 Confiodlen le urith olf 27 to - 2.05198 is 95 Confrolen e intenval tor tlope 16017 4 02.0518 x O 6176 Co 3345, 2.8629) vi The regremon model is 12.689o+ 1.601FX mas eggs 6mg 22.30 for mas 1