Could you please explain the answers. Thanks! 6. The statistical model for simpl
ID: 3055729 • Letter: C
Question
Could you please explain the answers. Thanks!
6. The statistical model for simple linear regression is written as ' o + Ax, where represents the mean of a Normally distributed response variable explanatory variable. The parameters P, and B, are estimated, giving the regression model defined by y-70 + 10x with standard deviation = 5. What is the distribution of the test statistic used to test the null hypothesis Ho: 0 against the alternative hypothesis Ha: 1 > 0? (Note: Assume n is the sample size.) and x represents the B) N(0,2) C) t(n-1) D) t(n -2) 7. Suppose we are given the following information: Sample size, n, = 100 Standard error of slope of the regression line, SE2 y = 100 + 4x Would a 95% confidence interval for be larger, smaller, or the same as an 80% confidence interval for p1? A) Larger B) Smaller C) Same D) It cannot be determined from the information given.
Explanation / Answer
Ans:
6)Option D is correct.
t(n-2)
Explanation:
Degrees of freedom. For simple linear regression (one independent and one dependent variable), the degrees of freedom (DF) is equal to:
DF = n - 2
where n is the number of observations in the sample.
Test statistic. The test statistic is a t statistic (t) defined by the following equation.
t = b1 / SE
where b1 is the slope of the sample regression line, and SE is the standard error of the slope.
7)As,critical t value will be larger for 95% CI as compared to 80%,so 95% confidence interval will be larger or wider as compared to 80% confidence interval.
Option A is correct.