In simple linear regression, you are told that the estimate of the slope coefficient was 0.9 and that the "t-statistic" for testing whether the slope parameter was unity or not was -2.7. What is the estimated standard error for the estimated slope coefficient? (The answer should be correct to two decimal places.)

A UQ master student collected data on annual wages (Y, in $'000) and years of study (X) from a random sample of 10 part-time workers to test this proposition. Assuming a linear relationship between Y and X, the student used a least-squares method and found that the Y intercept = -21.50 and the slope = 9.73. The student also found that the standard error of the slope was 1.61. Based on this information, what is the value of the t test statistic if you are testing the null hypothesis that there is no linear relationship between the two variables, X and Y? Round your final answer to three decimal places.

A consumer's spending is widely believed to be a function of their income. To estimate this relationship, a university professor randomly selected 19 of his students and collected information on their spending (Y, in dollars) and income (X, in dollars) patterns in week 6 of the semester. Assuming a linear relationship between Y and X, the professor used the least-squares method and found that the Y intercept = 20.90 and the slope = 0.66. The professor also found that the standard error of the slope was 0.08. Based on this information, what is the value of the t test statistic if you are testing the null hypothesis that there is no linear relationship between the two variables, X and Y? Round your final answer to two decimal places.

Assume the simple regression model holds. If the 95% confidence interval for the slope in an estimated simple regression is the interval (10, 22), then _________. a. the true (population) slope is not zero b. the F statistic of the fitted regression model is less than 4. c. the p-value of the estimated slope is more than 0.05. d. the t statistic for the estimated slope is approximately 2.

Let's correct the calculation for the standardized test statistic (t) in step iv. ### iv) Standardized Test StatisticThe standardized test statistic (t) is calculated as: \[ t = \frac{\bar{D} - \mu_D}{s_D / \sqrt{n}} \] Under the null hypothesis, \( \mu_D = 0 \): \[ t = \frac{-2.17 - 0}{1.93 / \sqrt{6}} \] First, calculate the standard error: \[ \text{Standard Error} = \frac{s_D}{\sqrt{n}} = \frac{1.93}{\sqrt{6}} = \frac{1.93}{2.45} = 0.787 \] Now, calculate the t-value: \[ t = \frac{-2.17}{0.787} = -2.76 \] The correct value for the standardized test statistic is \( t = -2.76 \). ### v) P-value for the Standardized Test StatisticFor a two-tailed test with \( t = -2.76 \) and \( df = n-1 = 5 \): Using a t-distribution table or calculator, the p-value for \( t = -2.76 \) with 5 degrees of freedom is approximately 0.020. ### vi) ConclusionBased on the p-value (0.020), which is less than the typical significance level of 0.05, we reject the null hypothesis. This suggests that there is a statistically significant difference in the reading age between the experimental group and the control group. So, the correct standardized test statistic should be \( t = -2.76 \). Let's fill in the correct value for the standardized test statistic in the image: \[ t = -2.76 \] This should be entered in the box for the standardized test statistic.

Human capital theory suggests that those who have invested in higher levels of education will be able to command higher wages. A labour economist collected data on annual wages (Y, in $'000) and years of study (X) from a random sample of 12 employees to test this proposition. Assuming a linear relationship between Y and X, the labour economist used a least-squares method and found that the Y intercept = -23.50 and the slope = 9.73. The labour economist also found that the standard error of the slope was 1.61. Based on this information, what is the value of the t test statistic if you are testing the null hypothesis that there is no linear relationship between the two variables, X and Y? Round your final answer to two decimal places.