STA 215P Using Technology to Produce Scatterplots and Regression Equations
We are going to look at data from http://brickset.com, which is a website dedicated to information about Lego sets. We are going to look at a small portion of this data set. We are going to focus on nine sets from the Pharaoh’s Quest collection. You can look at the sets by visiting https://brickset.com/sets/theme-Pharaoh-s-QuestThe data is given below.
| Set Name | Scarab Attack | Golden Staff Guardians | Flying Mummy Attack | Cursed Cobra Statue | Rise of the Sphinx | Scorpion Pyramid | Desert Glider | Desert Rover | Skeleton Mummy |
| Number of Bricks | 44 | 70 | 125 | 213 | 527 | 792 | 33 | 34 | 29 |
| Price in Dollars | 5 | 10 | 20 | 30 | 50 | 100 | 0 | 0 | 15 |
- Below is a Scatterplot of the data, label each of the points with the name of the corresponding set.
- Lego is coming out with a new set containing of 400 pieces.
- Draw a vertical line on the plot corresponding to 400 pieces.
- Using only the data points, can you say how much the new set should cost?
- What could we use to predict how much the new set should cost?
- Write out the equation of the regression line using the letter a as a placeholder for the intercept and the letter b as a placeholder for slope. Next to each symbol label what the symbol represents.
In order to find the regression line, we need to find a line which minimizes the sum of the square residuals. First, we will review what a residual is.
- Using the plot find the following:
- Using only the plot, what is the predicted cost for a set containing 213 pieces? The dotted lines on the plot are there to help you. Round your answer to the nearest integer.
- What is the observed cost for a set containing 213 pieces? Note the Cursed Cobra Statue has 213 pieces.
- What is the residual for this point?
- If you were going to calculate the sum of squared residuals for this line, how many residuals would you need to calculate?
Finding which line is the regression line can be difficult to compute by hand. You have a sheet that shows multiple ways to calculate the regression line. We will look at StatKey.In order to find a regression line in StatKey complete the following steps:
- Go to http://www.lock5stat.com/StatKey/.
- Click on 2 quantitative variables.
- Click on Edit data.
- Enter the data (The image shows what the form of the data should look like).
- Click OK.
- Click on Show regression line.
When using StatKey, you always want to do some quick checks to make sure that the data was entered correctly.
- Look at the plot. Are the explanatory and response variable correct? If they are switched, you can click on “switch variables” to fix.
- Look at the sample size. Does the sample size match the number of data points in your data? You should have 9 data points.
- Use the output to determine the correlation between these two variables. What is the appropriate symbol for the correlation coefficient?
- Write out the equation of the regression line using the intercept and the slope from the output.
- Using the equation, what is the predicted price for a set containing 700 pieces?
- Using the equation, what is the predicted price for a set containing 1000 pieces? Should we trust this prediction?
- What is the interpretation of the slope in context?
- Does it make sense to interpret the intercept in this case? Why or why not?
