IMPORTANT NOTE 2: When you are asked to calculate an answer by hand, you may still use your calculator for basic calculations (e.g. multiplication, division, taking a square-root etc.) Your workings should show that you know how a formulae or process works. 1. Consider the two linear equations below: Y = 5 - y = -3x-18 (1) (2) Draw both of these linear equations on the blank plot below (i.e. your answer should have two different straight lines on this blank plot). You must use the plot below to draw your lines. No other plot is allowed. (5 marks for each line for a total of 10 marks) y 45 40 35 30 25 20 15 10 5 0 0 2 6 + x x 00 8 10 12 2. This question is similar to the type of question you may encounter in one of the online numeracy quizzes. However, while the numeracy quiz requires an answer only, for this assignment submission you must also include your workings. Find the slope and the intercept of the straight line (i.e. the linear equation) containing the points (2,-5) and (-2, -10). (10 marks) 3. Below are six different scatterplots. In a random order, the correlations associated with these scatterplots are 0, -0.6, -0.9, 0.5, 0.8 and -0.3. Your task is to correctly match these correlations with the correct scatterplot. Each correlation belongs to just one scatterplot. When you are confident with your answers then write down the correct correlation for each scatterplot on the next page. (6 marks) Scatterplot A Scatterplot B Scatterplot C Scatterplot D Scatterplot E Scatterplot F Scatterplot A: correlation Scatterplot B: correlation: Scatterplot C: correlation Scatterplot D: correlation: Scatterplot E: correlation= Scatterplot F: correlation 4. The variable # of Influenza Cases in Table 1 located at the end of this question sheet measures the number of influenza cases, in 2019, per 1 million members of the population for a country. This data was collected from the World Health Organization (WHO) website, https://www.who.int/en/. For this question you are going to choose another variable measured for the countries listed in Table 1 to see whether your chosen variable correlates with the number of influenza cases. Marks will not be allocated according to whether there is correlation present, but whether the data collected is appropriate. For the data to be appropriate the following must hold: The data you collect for this question needs to be easily accessible, for us to check, for at least 10 of the countries that are listed in Table 1. This also means that the data must be actual measurements associated with these countries. The data you collect must be measured no earlier than the year 2019. Also, the variable must be in the same units for each of the countries. For example, if you choose a variable that is measured per 10 million members of the population for one country, then you need to also record the data for all other countries in units of per 10 million members of the population. The variable you select must not be Population Density which is the number of members in a population per square kilometre of the country. This is the variable I selected for my model answers. Complete the following questions. (a) Briefly describe below the new variable that you have chosen including (i) the units it is measured in and (ii) where you found the data. (b) At the end of this question sheet you will find Table 1. Enter the values that you have collected for your new variable under the columns called New variable where the new variable value for each country needs to appear in the space provided to the immediate right of the country name. (4 marks) (c) Enter the data from your completed Table 1, including the data for your new variable, into Excel and create a scatterplot of the two variables making sure that you include appropriate axis labels. Copy and paste this scatterplot into your assignment solutions document. (4 marks) (d) Using Excel, calculate the correlation between these two variables. What is it equal to and what Excel formula did you use to obtain it? (6 marks) Question 1: The standard format that I am going to compare with is: (y = mx + b) Where, (m) = slop; (b) = y-intercept For equation 1, -8y + 320 = 16x -8y = 16x - 320 y 16x-320/-8 y=-8 (-2x+40)/-8 y = -2x+40 = So, slop (m) -2; y-intercept (b) = 40 For equation 2, -y/5-x=-9 -y/5=-9+x -y=5(-9+x) -y=-45+5x Y = -5x+45 = So, slop (m) -5; y-intercept (b) = 45 15 40 35 y = -2x+40 30 15 220 25 15 10 5 0 2 9 Y = -5x+45 10 12 Question 2: The following formula is to get the slope of a line passing between two specified points: Slope = (change of y)/(change of x) Let's take the first point (x1,y1) = (-8, 3) and the second (x2, y2) = (2,-4). Then we may enter the values, Slope = (y2-y1)/(x2-x1) = (-4-3) / (2 - (-8)) = (-7)/10 So, the slope of the line: -7/10. We may use the point-slope form of the equation of a line to get the intercept: Y - Y1 = m(X-X1) Where (m) is the slope that we just found and (X1, Y1) is one of the provided locations. Using the first point (-8, 3) we get: y-3-(-7/10)(x-(-8)) y 3 (-7/10)x - 56/10 y = (-7/10)x - 13/5 So, The slop = (-7/10); The intercept of the straight line = (-13/5) Question 3: Scatterplot A: correlation = 0 Scatterplot B: correlation = 0.95 Scatterplot C: correlation = -0.95 Scatterplot D: correlation = 0.5 Scatterplot E: correlation = 0.3 Scatterplot F: correlation = -0.6 Question 4: a) The new variable that I have chosen is the number of fatalities owing to cardiovascular disease per 1 million people in 2019. I discovered this information on the World Health Organization's (WHO) Global Health Observatory (GHO) website. b) STA1DCT Assignment 3 Name: Neamul Hasan Student Number: 21400442 Country # of New variable Country Influenza # of Influenza New variable Cases per Cases per 1 mil 1 mil Argentina 2140.74 557 Pakistan 21.47 858 Australia 3642.79 238 Russia 131.99 1778 Brazil 85.47 276 South Africa 127.76 299 Canada 1139.89 259 South Korea 234.99 269 China 417.44 1146 United Kingdom 625.05 230 India 35.27 1030 United States 4781.93 301 Japan 76.75 390 Uruguay 345 460 Mexico 237.33 272 Table 1: Number of Influenza Cases for 2019. c) Scatterplot of the two variables: Country 2000 1800 1600 1400 1200 1000 800 600 400 200 0 0 1000 2000 3000 4000 5000 6000 New variable d) I calculated the correlation between the two variables using Excel's "CORREL" tool. The association between the number of influenza cases and the number of cardiovascular disease fatalities per 1 million people is (-0.29779). The Excel formula I used to get it is: =CORREL(B2:B16, C2:C16). e) According to the scatterplot, I see in the correlation value is -0.29779. It indicates that when the number of influenza cases rises, there is a tiny tendency for the number of fatalities from cardiovascular illnesses to rise as well. It's also can be noted that the link is weak. It is critical to highlight that correlation does not imply causation, thus we cannot infer that influenza causes cardiovascular disease just based on this research.