Assignment-5

2B03 Assignment 5 Regression Modeling and Prediction (Chapters 10 & 11) Matthew Musulin 400329990 Due Thursday December 2 2021 Instructions: You are to use R Markdown for generating your assignment output file. You begin with the R Markdown script downloaded from A2L, and need to pay attention to information provided via introductory material posted to A2L on working with R, R Markdown, and downloading data from ODESI. Having downloaded all necessary files, placed them in the same folder/directory, and added your answers to the R Markdown script, you then are to generate your output file using “Knit to PDF” and, when complete, upload both your R Markdown file and your PDF file to the appropriate folder on A2L. 1. Define the following terms in a sentence (or short paragraph) and state a formula if appropriate (this question is worth 5 marks). i. Test of Significance A formal procedure for comparing observed data with a hypothesis we want to prove true. The hypothesis is usually a statement about the population parameters. The results of the test are expressed in terms of a probability that measures how well the data and the hypothesis agree. ii. Coefficient of Determination The measure of how well an estimated regression line fits the sample data. R 2 = SSM/SST iii. Multiple Regression Analysis When there are several explanatory variables this is known as multiple regression analysis. iv. Individual Prediction Interval An estimate of an interval in which future observations will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis. 2. An economist is studying the relationship between unemployment and inflation, and has collected the following data. Inflation appears in columns, unemployment in rows (this question is worth 5 marks). Unemployment Abated Inflation Unchanged Accelerated Total Lower 5 5 10 20 Unchanged 5 35 20 60 Higher 20 0 0 20 Total 30 40 30 100 The data in the table above summarize the relationship between unemployment and inflation based on 100 months of data. For instance, for 35 months, inflation and unemployment were unchanged, while for 10 months inflation had accelerated and unemployment was lower. 1

Using the data in the table above, conduct an appropriate hypothesis test of independence between inflation and unemployment at the 5% level of significance. row1 = c( 5 , 5 , 10 ) row2 = c( 5 , 35 , 20 ) row3 = c( 20 , 0 , 0 ) Matrix = matrix(c(row1, row2, row3), nrow= 3 , byrow= TRUE) chisq.test(Matrix, correct= TRUE) ## ## Pearson ' s Chi-squared test ## ## data: Matrix ## X-squared = 65.278, df = 4, p-value = 2.249e-13 Therefore, because the p-value 2.49e-13 < 0.05, we reject H0. There is sufficient evidence that indicates a dependence between unemployment and inflation and the result is statistically significant. 3. Consider the following dataset on the final grade received in a particular course ( grade ) and attendance ( attend , number of times present when work was handed back during the semester out of a maximum of six times). Note that R has the ability to read datafiles directly from a URL, so here (unlike the odesi data that you manually retrieved) you do not have to manually download the data providing you are connected to the internet (this question is worth 5 marks). course <- read.table( "https://socialsciences.mcmaster.ca/racinej/files/attend.RData" ) attach(course) i. Run a regression of grade on attend using the R command lm() . What is the impact of a 1 unit increase of attend on the expected grade based on your model? attach(course) ## The following objects are masked from course (pos = 3): ## ## attend, grade lm(attend~grade) ## ## Call: ## lm(formula = attend ~ grade) ## ## Coefficients: ## (Intercept) grade ## -0.53515 0.05971 Therefore, a one unit increase in attendance will increase the probability of getting a higher mark. i. In class we distinguished between correlation and causation and cautioned against inferring causation from statistical correlation. Do your results suggest that an individual who increased their attendance by 1 unit would also experience an increase in their expected grade? Why or why not? Explain the roles of confounders in this context (e.g. along the lines of Sir. R. A. Fisher’s concerns). A correlation between variables does not immediately mean that the change in one variable is the cause of the change in the values of the other variable. Causation shows that one event is the result of the occurrence of the other event. In this case, the results show that the increased attendance would also experience a higher expected grade. 2