12. We are interested in predicting a college freshman's GPA for their first semester from their...

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12. We are interested in predicting a college freshmans GPA for their first semester from their overall ACT test score using

c) (5 pts. Now suppose we wish to estimate the slope of the least squares linc utilizing a 95% confidence interval. Are any a

math Statistics-And-Probability

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Answer 1

Answer #1

(a)

Conditions we need to consider before we find the least square line:

(i) Linearity: The data should show a linear trend as can be checked by scatter plot and be evaluating correlation coefficient which should be strong,i.e., absolute value near 1.0.

(ii) Normality: The residuals should be nearly normal.

(iii) Homoscedasticity: The variability of the points around the least square line remains roughly constant.

(iv) Independene: Observations are independent of each other.

(b)

Conditions we need to consider before we predict a student's first year GPA:

If we predict a student's first year GPA for any intermediate values of ACT test score (interpolation), the prediction is valid. If we predict a student's first year GPA for any values outside the given ACT test score (extrapolation), the prediction is not valid.

(c)

Conditions we need to consider before we estimate 95% confidence interval for slope of the least square line:

(i) The Dependent Variable (here: ACT test score has a linear relationship to the Independent Variable: here:first year GPA.

(ii) The Y values should be roughly normally distributed. For large samples(n > 30), slight skewness is permitted.

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