Boreal mixedwood forests have been commercially logged for conifers, transected by roads and seismic cutlines, and regionally

Question:

Boreal mixedwood forests have been commercially logged for conifers, transected by roads and seismic cutlines, and regionally fragmented by agricultural practices. Most recently, Alberta's public mixedwood forests have been allocated for harvest of trembling aspen for pulp, paper, and oriented strand board products. With relevance to commercial forestry, this report describes the structure and biodiversity of aspen- dominated mixedwood forests of fire-origin. The boreal mixedwood forest in Canada extends from south-western Manitoba, through the central and northern parts of the Prairie provinces, and into north-eastern British Columbia. Suppose the following data is collected from boreal mixedwood forests in northern Saskatchewan. Use the data in the following table to fit a linear regression model to predict Age using the rest of the variables. image text in transcribed

a. Plot the data and see if a linear regression model can be fit to predict age from the other variables.

b. Fit linear regression models considering each independent variable separately and test for their significance.

c. Build a model taking into account all three independent variables and their interac- tions. Use the overall F test to determine whether the model contributes significant information for the prediction of y. Use a = 0.05.

d. Carry out three separate tests with a significance level of 0.05 to decide if x1, x2, and X3 are significant.

e. Now fit a model with only x1, x2, and x1x2, (interaction effect) to predict age. How does this model perform compare to the one in (part c)?

f. How would you interpret the regression parameters B1, B2, B3, with reference to the model in (part e)? g. Does the effect of the quadratic term on predicting age in (part

e) appear to be use- ful? Use a = 0.05. How well does the model fit? Use any relevant statistics and diagnostic tools to answer this question. h. What do the residual plots tell you about the validity of the regression assumptions in (part e)? i. Based on the model in (part e), which of the predictors make the most significant contribution in predicting the dependent variable Y? Justify your answer. j. Is there any significant interaction effect of the independent variables on age in the model considered in (part e)? k. Suppose you suspect that independent variable x2 affects the response Y, but the relationship is curvilinear. Add the quadratic term that is in the model described in (part e). Use p-value approach to test the effect of the quadratic term on predict- ing age. 1. Which model would you prefer for prediction of age among the above three mod- els considered? Use the best model to obtain a point prediction of age that has DBH = 8, Canopy Height 15, and Stem Density = 4900. Also obtain a 95% confidence interval for the prediction. m. Suppose we wish to investigate the value of regressor variable x3 given that the regressors x and x2, and their interactions (xx2) are in the model. Perform the appropriate test of hypothesis to determine whether the reduced model is adequate. Use a = 0.05.