Understanding Regression, Correlation, and PMCC

Regression and Regression and correlation correlation

1 Given that ? = ??? where ? and ? are constants, what would you plot in order to get a straight line graph? ? against ? ? against log(?) log(?) against ? log(?) against log(?)

2 Given that ? = ??? where ? and ? are constants, which of these is the correct rearrangement to form a straight line? log ? = ???? ? ? log ? = ???? ? + log(?) log ? = ????(??) log ? = ? + log(?)

3 What value for the Product Moment Correlation Coefficient indicated that there is no correlation between two variables? 1 1 0 1000

4 Which of the following PMCC coefficient best matches the scatter graph? 0.94 0.9 0.3 9.1

5 Some data has been taken from the large data set on daily total rainfall (? mm) and daily total sunshine (? hours) in Leeming in July 2015 and has been plotted on a scatter graph. What is the most likely PMCC value? 1 0 0.65 0.65

6 Elizabeth is studying the price and number of pages of a random sample of books in a popular book store in the UK. She calculates the value of the PMCC between the price and number of pages in each book as 1.02. Which statement best describes the value 1.02? Definitely correct Probably correct Probably incorrect Definitely incorrect

7 The scatter graph illustrates the scores of 10 students in Maths and English exams at a school in Birmingham. Andrew calculate the correlation coefficient to be 0.570. Andrew removes the outlier P from the data. State the effect this would have on the PMCC value. PMCC would stay the same PMCC would decrease PMCC would increase PMCC would significantly increase

8 Using a calculator, work out the value of the PMCC for the following data: 0.818 70 0.856 0.7

9 The PMCC for 10 pairs of bivariate data (?,?) was calculated to be 0.2. If the ? and ? values are all doubled, what is the new value for the PMCC? 0.1 0.2 0.4 0.8

10 The temperature (?) is measured for 12 days against the number of ice creams solve (?). The data is shown below. ? = 1.68? 3.55 ? = 1.68 3.55? ? = 0.793? 24.2 ? = 0.374? + 8.52

11A zoologist believe that there is a positive correlation between the lengths and masses of trout in a river. She decides to carry out a hypothesis test to see if there is evidence for her claim. State the hypotheses for this hypothesis test. ?0:? = 0,?1:? > 0 ?0:? = 0,?1:? 0 ?0:? = 0,?1:? 0 ?0:? = 0,?1:? > 0

12Fred is interested in whether there is a relationship between the Engine size of a car and the Fuel economy. He decides to do a hypothesis test to decide whether or not there is evidence of correlation. State the hypotheses for this hypothesis test. ?0:? = 0,?1:? < 0 ?0:? = 0,?1:? 0 ?0:? = 0,?1:? 0 ?0:? = 0,?1:? < 0

13A population of students each took two different tests. A sample of 30 students was taken from the population and their scores on the two tests were recorded. A PMCC of 0.4125 as calculated. Test whether or not this shows evidence of positive correlation at the 5% level of significance. 0.4125 > 0.3610 Sufficient evidence to reject ?0 0.4125 > 0.3061 Sufficient evidence to reject ?0 0.4125 < 0.4629 Insufficient evidence to reject ?0 0.4125 > 0.2407 Sufficient evidence to reject ?0

14Birmingham city council collects data on the population densities in different areas of the city, in people per hectare, and the distances of those areas from the city centre, in km. It calculates the PMCC between the two sets of data and finds it to be 0.532. Given that the council collected data from 25 sample areas, test at the 1% significance level, the claim that there is a negative correlation between population density and the distance from the city centre. 0.532 < 0.5052 Sufficient evidence to reject ?0 0.532 < 0.2653 Sufficient evidence to reject ?0 0.532 < 0.4622 Sufficient evidence to reject ?0 0.532 < 0.3365 Sufficient evidence to reject ?0