Question

1.why we often use the t-distribution to perform hypothesis tests rather then the normal distribution?

2.state the assumptions of the simple regression model in terms of the individual observations，Yi for i=1 . . . n.

Answer 1

1.

Since people often prefer to use the normal, and since the t-distribution becomes equivalent to the normal when the number of cases becomes large, common practice often is:

• If σ known, then use normal.

• If σ not known:

If n is large, then use normal.

If n is small, then use t-distribution.

2.

The regression has five key assumptions:

Linear relationship
Multivariate normality
No or little multicollinearity
No auto-correlation
Homoscedasticity

The Yi values are indepedent and whch are dependent on Xi's