Question

Using data from 200 students, the expected score in the report for the student i got Xi degree in social sciences, which follows the model the linear model ŷi = β̂0 + b̂1Xi calculated by the method of simple least squares and is given by the formula: ŷi = 24,792 + 0,534 Xi The coefficient of determination R was also calculated R^2 = 0.3658. Answer the following questions: i. Interpret parameter b'1 (slope) of regression. ii. Interpret parameter b'0 (constant) of regression. iii. If the standard deviations of the two variables are SX = 10.7358 and SY = 9.4786 and it is known that the relationship between the two variables is positive, confirm numerically that b1 = 0.534 using the formula: β̂1 = (SY/SX)r. iv. If the sample mean values of two variables are X̅ = 52.405 and Y̅ = 52.775, then confirm numerically that parameter β̂0 = 24.79.

          Using data from 200 students, the expected score in the report for the student i got Xi degree in social sciences, which follows the model the linear model ŷi = β̂0 + b̂1Xi calculated by the method of simple least squares and is given by the formula:
ŷi = 24,792 + 0,534 Xi
The coefficient of determination R was also calculated R^2 = 0.3658.
Answer the following questions:
i. Interpret parameter b'1 (slope) of regression. 
ii. Interpret parameter b'0 (constant) of regression. 
iii. If the standard deviations of the two variables are SX = 10.7358 and SY = 9.4786 and it is known that the relationship between the two variables is positive, confirm numerically that b1 = 0.534 using the formula: β̂1 = (SY/SX)r.
iv. If the sample mean values of two variables are X̅ = 52.405 and Y̅ = 52.775, then confirm numerically that parameter β̂0 = 24.79.

Added by Ramon M.

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