The weekly statistics about number of passengers (Y in 1000s)per week in terms of the number electric train cars (X) werecollected through 30 weeks. The data were collected to assess therelationship between the number of passengers and the number ofelectric train cars. The process of data indicates the followingresults:

ΣX= 2589, ΣY= 762.748,ΣX^²=373055

ΣY^²=34905.9243 ΣYX= 112979.248

Σ(Y-Ya)*(X-Xa)= 14241.5194,

Σ(X-Xa)^² =37908.95

SST= 5816.7, SSE= 466.488, SSX= 37908.95

Where: Xa stands for Average of X

Ya Stands for Average of Y

For any hypothesis testing undertaken in this model,use the level of significanceα=5%

1. What is the expected sign of the independent variable?
2. Develop the linear regression model Using the least squaremethod of estimation and interpret the meaning of the intercept andthe regression coefficient.
3. Compute R² and interpret its meaning
4. Is the number of passengers sensitive to the number of electrictrain cars?
5. Compute the confidence interval of regression coefficient andinterpret its meaning
6. Forecast the dependent variable if the independent variable is165.
7. Find out and interpret the confidence interval of the predictedvalue computed in question (6).
8. Based on the previous questions, how well the model fits tothis phenomenon