1. Read the Case: Statistics In Action: Legal Advertising—Does It Pay? Summarize what the case is about, and what the variables represent by using paragraph. Please see the attachment for the case. Also Student A,B,C are the post by my classmates for your reference.
Student A: This article is about two partners working together. Lawyer A and Lawyer B. Upon separation the two lawyers had acquired advertising expenses that were unpaid. Lawyer A sued Lawyer B because he/she felt the advertising brought in mostly cases that Lawyer B dealt with. Lawyer A dealt with personal injury and lawyer B dealt with workers compensation. The variables represent cases that were tried for each lawyer based upon personal injury or workers compensation. The cases are shown over a 42 month period and how much advertising was spent each month for six months.
Student B:The pearson correlation between total advertising expenditure and new personal injury cases is 0.202 according to minitab.The pearson correlation between total advertising expenditure and new workers compensation is 0.197.This tells me that there is a minutely closer correlation between ad expenditure and personal injury than ad expenditures and compensation. However, the pearson coefficient ideally wants to be closer to 1 or -1 to show a close correlation and .202 and .197 are far from both.
Student C:I got the same answers as you, and based on those answers and the scatter plots I would conclude that neither the New PI Cases nor the New WC Cases really share any correlation with the TotAdvExp, or if they did it was at different times and amounts. Perhaps partner A reached a diminishing returns point at $190,000 AdvExp or so, because between approximately $140,000 and approximately $190,000 his number of New PI Cases grew dramatically. But at no point did partner B experience any sudden change (+ or -) in New WC Cases; or at least it wasn't as apparent. Thoughts?
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2. Based on the following output( by Student D) of the hypothesis testings for the slope coefficients for model 1 and 2, please answer which independent variable should you use to predict the dependent variable?
Student D :
In the model 1. i.e. Personal injury and advertising expenditure and Model 2. Workers' compensation and advertising expenditure, the Dependent or Response variables (i.e. y )are new PI(personal injury)cases and new WC(worker's compensation) cases per month and Independent or Predictor variable (i.e. x) is 6 months advertising expenditure.
As we learned in this session that, Prediction about dependent (Y) variable from the given value of independent variable.
Simple linear Regression Equation: y=β0+β1x+ε
Y=dependent (variable to be modeled).
X=Independent(variable used as a predictor of Y).
e(epsilon)=Random error component.
β1(beta one)=Slope of the line.
β0(beta zero )=y-intercept of the line.
Now, objective is to determine one or both of dependent variables are statistically related to 6 month advertising expenditure. For that, I need to do two-tailed null hypothesis test, where α = .01
For PI cases, p-value is aprox 0, so there is sufficient evidence to reject null hypothesis because, p-value is less than α. On conclusion the no. of new PI cases is linearly related to Advertising expenditures.
and for WC cases, p-value is 0.725, so there is insufficient evidence reject null, as p-value is greater than α. On conclusion there is no evidence to conclude that new WC cases are linearly related to advertising expenditure.