Could you please explain the answers. Thanks! 6. The statistical model for simpl

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.

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