Instruction for exercise 3
- Question 1 deals with the issue of the relationship between two samples of data. For
example, suppose you have a company's monthly data on market share and advertising
expenditures and you want to determine if advertising expenditures affect (or are related
to) market share in the current or the following months.
- Scatter plot is a useful tool to display a possible relationship between two
variables. To create a scatter plot, first select (highlight) the two columns of data
which include the paired data of the two variables, then click the chart wizard, and
choose chart type of XY (Scatter).
- After you finish the scatter plot, you can add a best-fit line (trendline) on the chart.
Click on the chart (to select it) and then from the pull-down menu, choose Chart -
Add Trendline..., then from the Trendline dialogue box, choose Trend/Regression
type: Linear to plot a linear relationship. A relationship between two variables is
linear if as the value of the explanatory variable, x, increases, y change by a
constant amount. We normally describe a linear relationship as y = a + bx.
- Scatter diagrams are useful in identifying possible relationship between two
variables. However, scatter diagrams and their accompanying best-fitting lines do
not indicate quantitatively the strength of the linear relationship between two
variables. Correlation coefficients provide a numerical index that measures the
degree of the linear association between two variables.
- To calculate correlation coefficient, when sheet (not the chart) is active (e.g., you
have just clicked on the data sheet), from the pull-down menu, choose Tools -
Data Analysis... - Correlation.
- Question 2b
- Note the data in Question 2 are time ordered. Therefore, not only can we
examine the relationship between the pairs of number of two variables in
the same month, it is also possible to examine whether sale of a particular
month is really affected by the quota of the month before. It is reasonable
to expect that the effect of quote often takes time to impact on the actual
- To determine if the sale is affected by the quote of the previous month,
you might want to develop a new column of data for Quote (t-1) by
copying the original quote data and paste it onto a new column (possibly
just beside the column for "sale volume") and aim into the raw position
which is one raw below the original position. In this way, the sale volume
of a particular month is aligned with the quote one month before that.
- Create a scatter plot and calculate correlation coefficient from the data in
two columns for sale volume and quote(t-1).
- Question 2 asks you to compare the mean of two samples of data
- To perform a t-test, from the pull-down menu, choose Tools - Data Analysis... -
T-test: paired two sample for means. This t-test is sometime also called within
- To plot mean and standard error (SE), you have to calculate standard error (t-test
only gives you mean values for each of the two groups). From the pull-down
menu, choose Tools - Data Analysis... - Descriptive Statistics to perform this test
on both samples of data.
- To create a bar chart for mean and SE, you might want to create a new table to
include data for means and SEs for both groups.
- After you create the bar chart for mean, double click on the bar to open a dialogue
box which includes the function for Y error bars. From "Y error bars" menu,
choose "custom" to input the data address range for SE.