how to draw a scatter-plot
Assignment Tasks
1. This company believed that their average number of quarterly accidents was relatively stable at 56 accidents per quarter. For the last three years the company has insisted that all workers wear protective clothing at all times, including hard hats, steel-capped boots, strong gloves, protective glasses, and so on.
Determine the mean, standard deviation and standard error for the last three years of quarterly data. Use this information to carry out a t-test to see if the average number of quarterly accidents for the last three years is significantly less than 56.
2. Obtain a scatter-plot of the quarterly number of accidents vs working days lost WDL per quarter. Think carefully about which variable should go on the vertical axis – remember, it is the independent variable that goes on the horizontal axis (i.e. the x-axis). Make sure you label your axes properly and your graph has an appropriate title. Briefly describe the nature of the relationship between these two variables.
3. Using Tools>Data Analysis in XL carry out a regression analysis on these two variables. Copy the output into your assignment and use it to determine the following:
o Write down the regression equation
o State the R-Square value and the Standard Error and explain what they mean with respect to this data.
o Write down the value of the gradient of the regression line and explain what it means in this case.
o Is the constant or intercept value significant in this case? How do you know this?
o Briefly explain why you think this regression model is, or is not, a good model.
4. Obtain a time series plot of the number of accidents per quarter. Describe the nature of this time series and identify which of the four time series components are present in this case.
Compare the first half of the time series to the second half (i.e. the first three years with the last three years), and briefly describe any differences.
By right clicking on one of the data points, add a trend line to the time series, making sure you include the regression equation and the R-Square value. Interpret the meaning of the slope coefficient in this case and state whether or not this is good for the company.
Use the regression equation to de-trend the data placing the de-trended data in another column. Obtain a time series plot of the de-trended data and explain what it shows.
5. Using information from your analyses write a short concluding paragraph about whether or not the company has been successful in trying to reduce the number of quarterly accidents for its workers.
