Researchers are interested in investigating whether or not there is a relationsh

Question

Researchers are interested in investigating whether or not there is a relationship between the amount of hours spent studying for an exam, X, and the improvement in final exam score, Y. To do so, they obtained a random sample of 10 individuals and obtained the values of Xand Yfor each individual, and fit a linear regression model to the resulting data, as seen in the plot below. 0 2 46 8 10 12 The fitted regression line was found to be Y = 1.03 + 0.45 . X Assuming all the model assumptions are met, and the inference procedures are valid, then: a) What is the predicted value of Y, at X= 0.5? Round your response to at least 2 decimal places.

Explanation / Answer

a) y=1.03 +0.45x
Here x=0.5
so y=1.03 +0.45(0.5)
=1.03 +0.225
=1.255

b) Here we can see that the regression line doesnt fit to the data very well.
So its extrapolation can have misleading results
Hence
No,This is example of extrapolation and should be avoided as it can have misleading results

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