MTH 166 Introduction to Data Analysis with Excel

Microsoft Excel is to be used throughout the course to fulfill the objectives outlined below.

1. Picturing Data

1.1 Distinguish between two types of data: (a) categorical and (b) numerical.

1.2 Create bar charts and write an interpretation or answer follow-up questions based on the charts.

1.3 Create pie charts and write an interpretation or answer follow-up questions based on the charts.

1.4 Create histograms and write an interpretation or answer follow-up questions based on the charts.

Change interval size and/or number of intervals, noting changes in the output.
Comment on the various shapes.

1.5 Know the difference between a histogram and a bar chart and when to use one or the other.

2. Basic Statistics of Univariate Data

2.1 Compute the mean, median and mode. Write these statistics with units. Understand these measures of central tendency and know which is the best measure in a given context.

2.2 Compute the standard deviation (sample). Write the statistic with its unit. Understand this measure of dispersion and interpret it within the given context.

2.3 Relate (2.1) & (2.2) to a histogram (1.4) and write an interpretation or answer follow-up questions based on the histogram.

3. Basic Statistics of Bivariate Data

3.1 Create a scatter plot. Include a title and units on the x and y axes. Comment concerning a possible relationship.

3.2 Compute and interpret the coefficient of correlation with respect to the scatter plot and the given variables.

3.3 Understand when and where r is a legitimate statistic (linear relationship).

3.4 Understand the distinction between causation and correlation. Explain that correlation does not imply causation. Give examples of where correlation is not due to causation.

4. Modeling Process for Regression
Within Sections 5 (Linear Regressions) and 6 (Non-Linear Regression), the following Modeling Process will be utilized and emphasized.

Modeling Process for Regression

1. Create a scatter plot

2. Determine the equation of best fit

3. Compute r²

4. Perform the following verification process:

a. Substitute at least one given independent data value into the equation of best fit.
b. Compare the predicted value to the actual value for the given independent data value.

5. Based on (3) and (4) results; determine if estimation and prediction are justified.

5. Linear Regression

5.1 Compute the line of best fit: y = a + bx

5.2 Compute and understand the meaning of r2 in determining how good the fit is from the view point of output (y) to input (x).

5.3 Interpret the slope and y-intercept with units.

5.5 Understand the relationships among r, the slope (b = r (s_y/s_x) ), and the scatter plot.

5.5 Make predictions using y = a + bx and interpret the results.

5.6 Sketch the graph y = a + bx on the scatter plot.

6. Non-Linear Regression

6.1 Create a scatter plot whenever bivariate data is given.

6.1.1 Compute a polynomial y = ax2 + bx + c or y = ax3 + bx2 + cx + d fit the data.

6.1.1.1 Compute and understand the meaning of r2 in determining how good the fit is from the view point of output (y) to input (x).
6.1.1.2 Make predictions using y = ax2 + bx + c or y = ax3 + bx2 + cx + d and interpret the results.
6.1.1.3 Sketch the graph y = ax2 + bx + c or y = ax3 + bx2 + cx + d on the scatter plot.

6.1.2 Compute an exponential y = c eb x to fit the data

6.1.2.1 Compute and understand the meaning of r2 in determining how good the fit is from the view point of output (y) to input (x).
6.1.2.2 Make predictions using y = c eb x and interpret the results.
6.1.2.3 Sketch the graph y = c eb x on the scatter plot.

6.1.3 Compute a logarithmic y = c Ln(x) + b to fit the data

6.1.3.1 Compute and understand the meaning of r2 in determining how good the fit is from the view point of output (y) to input (x)
6.1.3.2 Make predictions using y = c Ln(x) + b and interpret the results
6.1.3.3 Sketch the graph y = c Ln(x) + b on the scatter plot

7. Given a scatter plot determine the best model, using the Modeling Process for Regression outlined above. This may involve trying several models.

8. Time Plots (Optional)

8.1 Create a time plot of data where the horizontal axis is time and the vertical axis is the variable being measured.

8.2 Write about any observed trends, such as cycles (distinct but irregular up and down movements)

8.3 Write an interpretation or answer follow-up questions based on the time plot

8.4 Understand cautions concerning time plots.

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