A simple linear regression model for marks (Yi ) and the hours of study (Xi) is

Question

A simple linear regression model for marks (Yi ) and the hours of study (Xi) is as follows:
Yi = 0 + 1 Xi + ei
where 0 and 1 are unknown parameters, and ei is the disturbance term.
The regression results are:

Regression Statistics___________

R Squared 0.8643
Standard error 9.4531
Observations 20
__________________________

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?

Explanation / Answer

(a) Here p - value for study hour is 0.07 that means the probability of correlation coefficient for study hour getting zero. Similarly, p - value for intercept is the probability of intercept being zero in the regression.

(b) R squared means, which is 0.8643 is here that 86.43% variation in marks(y) is explained by the variation in study hours (x)

(c) Here we can reach the conclusion about marks and study hours is that if we increase study hours, there will be increase in marks. That shows there is positive, linear relationship between two variables.

(d) Here if x = 20 hours

y^ = 30 + 2.5 * 20 = 80

(e) The prediction can be said reliable as the coefficient of determination R - square is quite high and that tell a strong relationship between two variables. So, prediction is somewhat reliable.

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