1. Construct and submit a scatter plot of y versus x. Does a simple linear regression model seem appropriate here?
2. Fit the simple linear regression model using the method of least squares, i.e., findthe least squares line, ˆy = βˆ0 + βˆ1x by using the software. Submit your solution (output).
3. In plain English, interpret the meaning of the slope parameter β1.
4. In plain English, interpret the meaning of the intercept β0. Does it have a practical meaning here?
5. Report the value of s; and then calculate s2 and SSE.
Part II. Suppose that you obtained the following summary quantities to estimate the parameters in a regression study. Assume that x and y are related according to the simple linear regression model ˆy = βˆ0 + βˆ1x.
n = 14, n
X
yi = 572,
i=1 n
X 2
yi = 23530,
i=1
, and .
Answer the following questions.
6. Calculate the least squares estimates of the slope and the intercept.
7. Estimate σ2. Hint: Use the following formula to calculate the sum of squared errors:
SSE = SSyy − βˆ1SSxy.
8. Use the equation of the fitted line to predict y at x = 3.7. Suppose that the observed (actual) value of y = 46.1 when x = 3.7. Calculate the corresponding residual.
