Problem: Mathematics department at a liberal arts college used a 25-point placement test to assist in assigning appropriate math courses to incoming freshmen. The department believes that the test is a good predictor of a student’s final numerical grade in its introductory statistical course. The results are shown below.

1. Construct a scatter plot for the data.
2. Find the least square line relating x to y .
3. Plot the least square line on the graph, part (a).
4. Interpret the values of \[{{\overset{\scriptscriptstyle\frown}{\beta }}_{0}}\] and \[{{\overset{\scriptscriptstyle\frown}{\beta }}_{1}}\] .

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: \[\hat{y}\] = \[{{\hat{\beta }}_{0}}\] + \[{{\hat{\beta }}_{1}}\] x .

n = 14, \[\sum\limits_{i=1}^{n}{{{y}_{i}}}\] = 572, \[\sum\limits_{i=1}^{n}{y_{i}^{2}}\] = 23,530, \[\sum\limits_{i=1}^{n}{{{x}_{i}}}\] = 43, \[\sum\limits_{i=1}^{n}{x_{i}^{2}}\] = 157.42, and \[\sum\limits_{i=1}^{n}{{{x}_{i}}}{{y}_{i}}\] = 1697.80.

1. Calculate the least square estimates of the slope ( \[{{\hat{\beta }}_{1}}\] ) and intercept ( \[{{\hat{\beta }}_{0}}\] ).
2. Estimate the variance of the error term,  ² .

Problem: Use Minitab to solve this problem. To examine the relationship between the size (in square feet) of a store and its annual sales (in thousands of Dollars), a sample of 14 stores was selected. The results for those 14 stores are summarized in the table below.

1. Fit the least squares line to the data to write the simple linear regression equation.
2. Plot the data and graph the least squares line as a check on your calculations.
3. Is the predictor "Size" significant at =0.05?
4. Interpret the meaning of the slope parameter  ₁ .
5. Evaluate the assumptions (check on  is i.i.d. N(0, ² )).
6. What are the values of SSE and s ² ? What does " s " mean?
7. What is the 95% Confidence Interval for the slope?

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Solution: The downloadable solution consists of 15 pages, 618 words and 6 charts.
Deliverable: Word Document