STATISTICS 1123 Correlation, Linear Regression, & Chi-Square Test 1. [10 marks] Sporty cars are designed to provide better handling, acceleration, and a more responsive driving experience than a typical sedan. However, even within this select group of cars, performance as well as price can vary. Consumer Reports provided road-test scores and prices for the following 12 sporty cars (Consumer Reports website, October 2008). Prices are in thousands of dollars and road-test scores are based on a 0-100 rating scale, with higher values indicating better performance. This dataset is stored on D2L, on our course website, under the folder 'Datasets' and it is called 'Assignment5_Question1.xlsx'. This dataset is in Excel format and before you analyze it, you need to import it into Statgraphics (you've done this process in Assignment 2 - please take a look at Assignment 2 tips if you need to remind yourself how to do this). a) Using Statgraphics software, plot a scatterplot with price as the explanatory (i.e. independent) variable and road-test scores as the response variable. With the scatterplot, also report the sample correlation coefficient, r. The commands for the scatterplot and how to obtain r, in Statgraphics can be found in our lecture notes on Scatterplots and Correlation Coefficient. [2 marks] b) What does the scatterplot developed in part a) along with the correlation coefficient r indicate about the relationship between the two variables? Make sure you comment on the direction, strength and potential outliers. [3 marks] c) Assess the statistical significance of the sample correlation coefficient, r using the table of decision points. State your conclusions. [3 marks] d) Why you should not estimate a linear regression equation for this data? [2 marks] 2. [13 marks] Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain. Data has been collected on 12 females and 6 males, and their lean body mass (in kg) and metabolic rate (in calories burned per day) were recorded. This dataset is stored on D2L on our course website, under the folder 'Datasets' and it is called 'Assignment5_Question2.xlsx'. This dataset is in Excel format and before you analyze it, you need to import it into Statgraphics (you've done this process in Assignment 2 - please take a look at Assignment 2 tips if you need to remind yourself how to do this). a) Using Statgraphics software, plot a scatterplot with mass as the explanatory (i.e. independent) variable and rate as the response variable. With the scatterplot, also report the sample correlation coefficient, r. [2 marks] b) What does the scatterplot developed in part a) along with the correlation coefficient r indicate about the relationship between the two variables? Make sure you comment on the direction, strength and potential outliers. [3 marks] 1 c) Assess the statistical significance of the sample correlation coefficient, r using the table of decision points. State your conclusions. [3 marks] d) What is the estimated regression equation for this dataset? What is the slope? Provide an interpretation for the slope of the estimated regression equation. [3 marks] e) Estimate y when x=43 and interpret your answer. [2 marks] 3. [10 marks] The General Social Survey asked 1,152 adults (selected using random sampling method) in Vancouver to react to the following statement: "It is right to use animals for medical testing, if it might save human lives." The purpose of the survey was to find out how do the distributions of opinion differ between men and women. Here is the two-way table of their responses: Response Strongly Agree Agree Neither agree nor disagree Disagree Strongly disagree Male Female 76 59 270 247 87 139 61 123 22 68 a) State the null and alternative hypothesis in this question. [2 marks] b) Calculate the Chi-square statistics (show your computations, i.e. work). [5 marks] c) Assess the statistical significance of the Chi-square statistic using the table of decision points. State your conclusions, that is to say state the statistical inference you would make based on these results. [3 marks] 2