The data for this prompt is based on a sample of 500 weekly measures of multiple broadway musicals (a different sample, but same population as Q1 on the Module 7 Problem Set). Below is the same scatterplot but with different colour (and shape) pallettes. The first looks at the weekly number of performances of the show per week against the average weekly price of a ticket. The second looks at the same, but colour coordinates for whether the data point was of the musical "Hamilton" or not. (Note, there was a lot of overlap of "number of shows" so the numbers have been jittered slightly to improve readability). 300 - 300- . . Hamilton 200 .'....Ag Average price of a ticket in a week Average price of a ticket in a week 200 - No Yes 100 - 100 - SC .. 0 0 2.5 5.0 7.5 10.0 12.5 2.5 5.0 7.5 10.0 12.5 Number of performances in a week Number of performances in a week 1. Write 1-2 sentences describing a possible reason which would explain why we observe that higher weekly number of performances tend to be associated with higher weekly average ticket price, based on the (first) scatterplot above. 2. In the Module 7, we talked about how we can visualize a simple linear regression model with one numerical predictor by plotting a straight line (the fitted regression line) on a scatterplot. Based off the above, do you think that the simple linear regression for Hamilton and non-Hamilton musicals is the same? If so, why? If not, what changes? Would the two groups have the same/similar intercepts? Would the two groups have the same/similar slope? If they are different how would they differ? How would you recommend visualizing this? Describe what the plot would look like in general (i.e. would there be more than one line? would the line(s) be straight? what would the slope(s) of the line(s) represent?)