A simple linear regression model for marks and the hours of

A simple linear regression model for marks (%) and the hours of study (X) is as follows Yi-po + 1 Xi + ei where 0 and 1 are unknown parameters, and ei is the disturbance term. The regression results are: Coefficient 30 2.5 Standard error t Stat 10 3.00 2.50 p-value 0.01 0.07 Intercept Study hour Xi Regression Statistics R Squared Standard error 9.4531 Observations 20 0.8643 a. Explain the meanings of the p-value for study hour and the p-value for intercept. b. Explain the meaning of R Squared c. What conclusions can you reach about the relationships between marks (Yi) and study hours (xi)? d. What is the predicted marks for a person with 20 hours of study? e. Is this prediction reliable?

Solution

a) As per the definition of p-value in statistics , it is a calculated probability . P-value denotes the level of marginal significance of a hypothesis test . It tells us the probability of the occurance of an event ( null hypothesis ) . It is used as a rejection parameter for the null .

If p-value is < 0.05 we reject the null . We consider that the null hypothesis here is no significant difference between the means . For the intercept term the p-value is 0.01 . Hence we reject the null in this case and say that the intercept term is significant . For study hours ( X) the p value is 0.07 which is > 0.05 . So we can say that X is not a very significant variable in the regression model .

b) R squared is a measure which tells us how near is the data to the fitted line . Here it is 0.8643 . So we can say that about 86.43 % of variation in the data can be explained by the model or the explanatory variables . So the model is a robust one .

c) By looking at the p value we can say that study hours is not so significant in determining marks .

d) Y = B0 + B1 . X1 ( 20 hrs of study ... X = 20) . This is predicted equation .

Hence Y = 30 + 2.5 . 20 = 30 + 50 = 80 units .

e) Yes the prediction is reliable because the R squared value is high .