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.

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.

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 upper critical value used to test the null hypothesis that there is no linear relationship between the two variables, X and Y at the 5% level of significance? Use our textbook statistical table to answer the question.

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 statistical decision would you made if you are testing the null hypothesis that there is no linear relationship between the two variables, X and Y? a. Accept the null hypothesis. b. Reject the null hypothesis. c. Do not reject the null hypothesis. d. Reject the alternative hypothesis.

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.)