Module 11
__ is the point estimate of the variance of the error term populations.
MSE
Match the following:
Mean square error: The point estimate of the variance of the error term populations. Standard error: The point estimate of the standard deviation of the error term populations.
Suppose you fit a regression line to 20 (x, y) pairs and find b1= 4.305 and sb1= 1.35. Given that for 18 df, t.025= 2.101 and t.05= 1.734, find a 95% confidence interval for β1.
[1.469, 7.141]
When testing H0: β1 = 0 versus Ha: β1 ≠ 0, the provided regression analysis is obtained. What is the 95% confidence interval for the slope?
[9.9533, 10.3393]
A 100(1 - α) percent confidence interval for the slope is ______
[b1 ± tα/2 sb1]
Simple linear regression results ______ sensitive to mild departures from the underlying assumptions.
are not
Suppose you fit a regression line to 15 (x, y) pairs and you find b0 = 7.8 and sb0= 12.6. Given that t.025 = 2.160 when df = 13, what is the t-statistic for testing H0: β0= 0 versus Ha: β0≠0 and what do you conclude at α =.05?
t = 0.62; do not reject H0; the intercept is not significantly different from 0.
When testing the significance of the slope, what is the test statistic used?
t = b1/sb1
When testing the significance of the slope, the test statistic is based on ______
the t distribution with n - 2 degrees of freedom.
The independence assumption in simple linear regression is most likely to be violated when ______ data are being used.
time-series
When a least squares line is fit to 10 observations, we obtain SSE = 888.96. Calculate the standard error, s.
10.54
When a least squares line is fit to 11 observations, we obtain SSE = 191.7017. Calculate the mean square error, s^2.
21.300
Which of the following are assumptions underlying simple linear regression?
At any given value of x, the population of potential error term values has a mean equal to 0. At each value of x, the population of potential error terms is normally distributed.
Which of the following are assumptions underlying simple linear regression?
At any given value of x, the population of potential error term values has mean 0. The values of the error terms are independent.
In a test of H0: β1= 0 versus Ha: β1≠ 0 based on n = 20 (x, y) pairs, the t-statistic is -2.05. Given that when df =18, t.025 = 2.101 and t.05= 1.734, what is the correct decision if α = 0.05?
Do not reject the null hypothesis; we cannot conclude a linear relationship exists between x and y.
When testing H0: β0 = 0 versus Ha: β0 ≠ 0, the provided regression analysis is obtained. What is the correct conclusion to the test at the 5% significance level?
The y intercept is significant.
When testing H0: β1 = 0 versus Ha: β1 ≠ 0, the provided regression analysis is obtained. What is the correct conclusion to the test at the 5% significance level?
There is a linear relationship between x and y.
