A researcher wants to analyze the data from different roller coasters. They use
ID: 3315963 • Letter: A
Question
A researcher wants to analyze the data from different roller coasters. They use the following variables: Type (Wooden versus Steel); Duration; Speed; Height; Drop Inversion (Yes or No) Look at the following graph of Height versus Duration. Height versus Duration (with least squares tit) 350 Y = 49.1 + 0.702x 300 250 200 150 100 50 160 180 200 220 240 60 80 100 120 140 Duration a. What factor could be causing the slight fan shape of these points? b. What can we do to correct for this in our regression?Explanation / Answer
a) A well-fitting regression model results in predicted values close to the observed data values.
The reason behind slight fan shape of the points is the relation is not linear to large extent. Coefficient of correlation is much less than 1. This happens because points are not distributed in exact direct proportion and their is some variance in the distribution.
b. To solve for linear regression we need to have minimum Mean square error. We plot the line such that MSE is minimum and points are distributed uniformly to get best fit line. But their are certain limitations of linear regression which cant be resolved. The only thing we can say is relation is not bit linear as coefficient of correlation is less than 1.
We can try for other modes of regression if it seems relationship is not linear
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