Question

Consider the given situation and the statistical summary and answer the following questions. Ecologists sometimes find rather strange relationships in our environment. One study seems to show that beavers bene fit beetles. The researchers laid out 23 circular plots each four meters in diameter, in an area where beavers were cutting down cottonwood trees. In each plot they counted the number (x) of stumps from trees cut by beavers and the number (y) of clusters of beetle larvae. Some descriptive statistics of the data are given. Descriptive Statistics: x, y Variable N 23 Mean 2.217 25.09 StDev Minimum 1.204 1.000 15.64 6.00 Q1 Median Q3 Maximum 1.000 2.000 3.000 5.000 12.00 21.00 40.00 56.00 y 23 Correlations: x, y Pearson correlation of x and y = 0.916 % (a) The regression equation is ĝ= (write in the form bo+b1*x, and keep at least 3 digits after the decimal point.) (b) Calculate the proportion of the variability explained by the regression line. (Enter your answer as a percent): (keep at least 3 digits after the decimal point.) (c) Predict the number of clusters of beetle larvae (i.e. y) for a plot with 2 stumps (i.e. X = 2). (keep at least 3 digits after the decimal point.)

Answer 1

a)

slope b1=r*sy/sx=			11.899
intercept bo=y̅ +r(sy/sx)*(x̅)=			-1.290

y^ = -1.290+11.899x

b)

proportion of variability explained =r² =83.906 %

c)

predicted value = -1.290+11.899*2 =22.508