Scatterplot of mean full versus assistant salaries

Assignment Help Basic Statistics

Reference no: EM13118774

Salary data for a sample of 50 universities were obtained. We are curious about the relationship between mean salaries for assistant professors (junior faculty) and full professors (senior faculty) at a given university. In particular, do universities pay (relatively) high salaries to both assistant and full professors, or are full professors treated much better than assistant professors? In other words, do senior faculty receive high salaries compared to other universities while junior faculty receive relatively low salaries? Suppose we fit the following simple linear regression model

Full Prof. Salaryi = β0 + β1(Asst. Prof. Salary)i + εi

where the deviations εi were assumed to be independent and normally distributed, with mean 0 and standard deviation σ. The variables Full Prof. Salary and Asst. Prof. Salary are the mean salaries for full and assistant professors at a given university. This model was fit to the data using the method of least squares. The following results were obtained from statistical software. Note that salaries were in thousands of dollars. Mean assistant professor salaries were treated as the explanatory variable and mean full professor salaries as the response variable.
R2 = 0.698
s = 5.640
Variable Parameter Est. Std. Err. of Parameter Est.
Constant -22.47 11.07
Asst. Prof. Salary 1.8393 0.1745
Here is a scatterplot of mean full versus assistant professor salaries (in thousands of dollars)

Which of the following statements is supported by the plot?

Reference no: EM13118774

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