Question: Consider the Redwood data set. We want to predict the Height (in inches) of redwood trees using Diameter (in inches) and Bark Thickness (in inches)

Consider the Redwood data set. We want to predict the Height (in inches) of redwood trees using Diameter (in inches) and Bark Thickness (in inches) as predictors.

(a)Using Google Sheets XL-Miner run and state the multiple regression equation.

(b)Interpret the meaning of the slopes in this equation.

(c)Predict the mean height for a tree that has a breast diameter of 25 inches and a bark thickness of 2 inches.

(d)Use the overall F-test to test whether there is a significant relationship between the Height of a tree and the two independent predictor variables. =0.05

(e)At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the independent variables to keep in this model.

(f)Report and interpret R Square (Coefficient of Multiple Determination).

(g)Report and interpret Adjusted R Square.

SUMMARY OUTPUT

Regression Statistics

Multiple R0.88645329

R Square0.78579943

Adjusted R Square0.76199937

Standard Error22.5985232

Observations21

ANOVAdfSSMSFSignificance FRegression233722.807216861.403633.016695449.49261E-07Residual189192.47855510.693253Total2042915.2857CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept62.141844713.50327684.601982580.00022128233.7725128190.511176533.772512890.5111765Diameter2.057191980.44280454.645824470.0002009641.1268942472.987489711.126894252.98748971Bark thickness15.63622737.148397932.187375060.0421548430.61800059230.65445410.6180005930.6544541

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