You conduct a study to see if the average number of hours spent studying (per we

Question

You conduct a study to see if the average number of hours spent studying (per week) varies by grade level. You ask a total of 160 students to report the number of hours they spend studying in a typical week. Students from all grade levels (freshmen, sophomore, junior, senior) are sampled. You run a linear model analysis, and get the following results:

(Please explain with great detail to further my understanding in linear regression and linear regression with categorical variables. Thank you.)

a. What are the dependent and independent variables in this model?

b. Interpret the coefficients. What do each of them mean?

c. According to the model, what is the estimated average study time for a junior?

d. Based on the results, what can conclude about student study time?

Coefficients Estimate Std. Error t-value p-value Intercept 8.0082 0.1484 53.954 <0.001 Grade:Sophomore 0.129 0.2126 0.607 0.545 Grade:Junior -2.0636 0.2062 -10.007 <0.001 Grade:Senior -2.1916 0.2126 -10.375 <0.001

Explanation / Answer

a) Independent variables: Grade:Sophomore,Grade:Junior,Grade:Senior

Dependent Variable: the number of hours they spend studying

b)

B0=8.0082, the Y-intercept, can be interpreted as the value you would predict for Y if both X1 = 0,X2 =0 and X3 = 0. We would expect an average number of hours spend on studying when all grad leves are equal to zero. However, this is only a meaningful interpretation if it is reasonable that both X1, X2 and X3 can be 0, then B0 really has no meaningful interpretation. It just anchors the regression line in the right place.

Interpreting Coefficients

Since X1 is a continuous variable, B1 represents the difference in the predicted value of Y for each one-unit difference in X1, if X2 remains constant. This means that if X1 differed by one unit, and X2 did not differ, Y will differ by B1 units, on average. Similarly, the meaning same for the remaining variables

c) The estimated average study time for a junior is -2.0636

d) P-value of Grade:Sophomore > alpha 0.05, we accept H0

Thus the variable Grade.Sophomore is not effected on the model

P-value of Grade:Junior < alpha 0.05, we do not accept H0

Thus the variable Grade.Junior is effected on the model

P-value of Grade:Senior < alpha 0.05, we do not accept H0

Thus the variable Grade.Senior is effected on the model

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