3. Colorado Snow. The file called co annual snoufall. JMP contains data on annua

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3. Colorado Snow. The file called co annual snoufall. JMP contains data on annual snowfall and elevation at 27 different locations in Colorado, both cities and ski resorts. Tourism is a very large part of the economy of the Rocky Mountain part of Colorado. Ski resorts and ski towns often boast of their annual snowfall. Often, the more snow, the better the economy does The mayor of Dillon believes some ski resorts and ski towns are inflating their annual snowfalls to attract more tourists. She wants to predict snowfall based on elevation where the annual snowfall comes from the National Weather Service (a) Identify the Explanatory and Response Variables. i. Explanatory (x): ii. Response (y): (b) Fit a least squares regression model to the data (in JMP) through the commands Analyze Fit Y by X, correctly casting the variables into their roles of ''Y', ald "X" Then select Fit Line from the "red triangle" menu. Using the output, report: (Round your answers to two decimal places.) i. The value of the sample intercept bo ii. The value of the sample slope bi ( (FREE RESPONSE) Interpret the intercept bo within the context of the problem. Make sure to also comment on whether or not the interpretation is meaningful within the context of the problem. (d) (FREE RESPONSE) Interpret the sample slope bi within the context of the problem (e) (FREE RESPONSE) What percentage of variation in your response variable can be explained by its linear relationship with your explanatory variable? Write your answer as a percentage and round to two decimal places, (eg. 34.21). Interpret this percentage in the context of this problem (f) (FREE RESPONSE) We have Created the residual plot using JMP by selecting Plot Residuals from the "red triangle" (Linear Fit) menu; this menu is available after fit ting the LS regression line from part (3b). The graph of residual plot (Residual by X Plot) Based on this residual plot, what is your comment on the fit of this model? is the following Residual by X Plot 50 50- 100 4000 6000 8000 10000 12000 4000 elevation

Explanation / Answer

a) EXPLANATORY VARIABLE (X): ELEVATION

RESPONSE VARIABLE (Y): SNOWFALL

b) y(hat)= 0.040996(elevation)-186.5583

y(hat)=0.040966x-186.5583

b0= -186.56 and b1= 0.04

c) INTERPRETATION OF b0:

B0, the Y-intercept, can be interpreted as the value you would predict for Y if X = 0

We would expect an average snowfall of -186.5583 for no elevation.. However, this is only a meaningful interpretation if it is reasonable that X is 0, and if the data set actually included values for X1 were near 0.

If none of these conditions are true, then B0 really has no meaningful interpretation. It just anchors the regression line in the right place.

d) INTERPRETATION OF b1= This means that if X differed by one unit Y will differ by 0.04units, on average.

e) Coefficient of determination r^2= 0.897909= 0.8978

89.78 % indicates that the model explains 89.78% of the variability of the response data around its mean.

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