Question

In: Statistics and Probability

1. Sample data on exam grades (Y), hours studied (X1) and homework average (X2) was used...

1. Sample data on exam grades (Y), hours studied (X₁) and homework average (X₂) was used to estimate the following regression equation:

Y-hat = 60 + 5X₁ + .1 X₂

a. Interpret the value of the estimated constant (a)

b. Interpret the estimated coefficient on X₁

c. Interpret the estimated coefficient on X₂

d. Predict the grade of a student who studied 5 hours and had a homework average of 90.

Please answer questions and show work.

Thanks

Expert Solution

regression equation:

Y-hat = 60 + 5X1 + .1 X2

a)

B0 that is Y-intercept, can be interpreted as the value you would predict for Y if both X1 = 0 and X2 = 0.

That is if hours of study and homework hours are 0 still particular student can obtained 60 grade.

b)

B1 represents the difference in the predicted value of Y for each one-unit difference in X1, if X2 remains constant.

That if for unit change in X1 the change in Y is 60 unit either increasing or decreasing.

c)

B2 is interpreted as the difference in the predicted value in Y for each one-unit difference in X2 if X1 remains constant.

That is for unit change in X2 the the change in Y is 0.1 unit either increasing or decreasing.

d) Predicted grade of student is

Y-hat = 60 + 5×5 + 0.1×90

= 94

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orchestra answered 1 year ago

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