Question

Question 3: The regression line equation for a set of data is given by y-hat = 2.3x+5 with n = 10. The mean value of y is 10.1 for the data set. Use a = 0.05. A. If the linear correlation coefficient is r=0.521, what is the best predicted y-value for x = 5? Justify for your answer. B. If the linear correlation coefficient is r = 0.972, what is the best predicted y-value for x = 5? Justify your answer.
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Answer 1

Answer:-

Given That:-

The regression line equation for a set of data is given by y-hat = 2.3(x) + 5 with n = 10. The mean value of y is 10.1 for the data set. Use a = 0.05.

A. If the linear correlation coefficient is r = 0.521, what is the best predicted y-value for x = 5? Justify for your answer.

Given,

0.05 level, two tail test and n-2 = 8 df,

Critical r = 0.632

Since correlation coefficient r < critical value

We can not use regression equation:

best predicted value = average of all data y values = 10.1

B. If the linear correlation coefficient is r = 0.972, what is the best predicted y-value for x = 5? Justify your answer.

Since correlation coefficient r > critical value:

We can use regression equation:

best predicted value = 2.3 * 5 + 5

= 16.5

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