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You are given a large sample of data to analyse using regression analysis.
a) Firstly, you wish to discover whether using simple linear regression analysis is appropriate. Which two graphs could you create with your data to help you? How would you interpret them?
b) You also decide to consider using a quadratic regression model. Write out the regression model for this case. The independent variable is x and the dependent variable is y.
c) How would you test whether the coefficient of the quadratic term was statistically significant at the 5% level?
d) How would you compare the two models in order to choose the most appropriate one?
e) Suppose that you wished to study differences in income in the UK. One of the factors which you believe is important is gender. You are given statistical data from a national survey. Respondents can state that they are male or female or refuse to disclose their gender. How would you incorporate gender into your regression equation or would you choose to discard it from your analysis?
f) What pitfall should you avoid with part e) above?
Since you have a significant effect you would need to run post-hocs here. Please determine the appropriate post-hoc for this situation and report the results in proper APA format.
What is the difference between a one-tail and a two-tail test? How do we identify each? What is meant by a p-value?
List 1 profession example for each probability type: empirical probability and theoretical (classical) probability. Explain clearly how these probabilities are used.
In a simple linear regression analysis of 18 data points the following ANOVA table was found.
A production line operates with a mean filling weight of 500 grams per container. Over filling or under filling presents a serious problem and when detected requires the operator to shut down the production line to readjust the filling mechanism.
Assume that x is an Independent variable and y is a dependent variable. Calculate the Pearson correlation coefficient. What does the correlation mean? Is the correlation statistically significant at the 5% level? What is the effect size? What is the ..
Computing the probability values using normal distribution - what proportion have SAT scores greater than 550?
You decide to predict gasoline prices in different cities and towns in the U.S. for your term project. Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income
Represent (X,Y) as a function of (U,V). Find the joint density f(u,v) for (U,V) (Hint: take into account the region where it is non-zero). Calculate f(1,0) and input it as the answer.
Conclude that the population average pulse rate is 71.8. Reject the hypothesis that the population average pulse rate is 70.
Analyze the above alternatives with utility function U(x) = 0.0085x - 6.725(ln(x)), where x is total/net wealth: If Nancy has $5,600, which alternative he should choose among A, B or C?
Independent random samples taken on two university campuses revealed the following information concerning the average amount of money spent on textbooks during the fall semester.
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