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# Find out whether, in general, more fat means more calories in food. I am doing this to discover which foods' calories are largely composed of fat, and which foods have many calories, and yet have only a small amount of fat, if any at all.

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Introduction

Statistics 2: Component 02: Coursework on Bivariate Data Aim The aim of this investigation is to find out whether, in general, more fat means more calories in food. I am doing this to discover which foods' calories are largely composed of fat, and which foods have many calories, and yet have only a small amount of fat, if any at all. The results I discover might be especially useful for people who are dieting. Often people avoid foods with fats in them, and this sort of investigation will help to show what foods are best for this diet. On the other hand, the information could also be used for people who are on low calorie diets, but that are not especially concerned with the amount of fat they get in their food. Data Collection I decided to use a range of 50 foods. The information source for this data was a book called 'Calorie Counter' which is a source with over 1200 foodstuffs' data recorded. To obtain the data, I took every 20th result from the book, however, if I got two pieces of data that were of the same food, the only differences being that they were made by different companies or with a specific flavour, I took the next food which I had not used before. ...read more.

Middle

Using the formula: Sxy SxxSyy The eventual result was that: r = 0.88622 We can do a one-tail 1% significance test to see whether this value is sufficiently high to show good correlation. Our hypotheses are: H0: There is no correlation H1: There is a positive correlation If we check the critical value for a 1% test, for n = 50, the critical value is 0.3281. As my value for r, 0.88622 > 0.3281 we accept the alternate hypothesis and reject H0. This shows that there is good correlation. X - x (X - x)^0.5 Y - y (Y - y)^0.5 (Y - y)(X - x) 476.26 226823.59 59.93 3592.08 28544.17 -159.74 25516.87 -12.67 160.43 2023.27 -197.74 39101.11 -12.37 152.92 2445.25 397.26 157815.51 49.93 2493.40 19836.78 280.26 78545.67 12.13 147.23 3400.67 2.26 5.11 -10.87 118.07 -24.56 148.26 21981.03 -6.07 36.80 -899.35 143.26 20523.43 -4.47 19.95 -639.80 220.26 48514.47 5.63 31.74 1240.94 152.26 23183.11 0.13 0.02 20.40 -180.74 32666.95 -12.57 157.90 2271.18 -137.74 18972.31 -11.47 131.47 1579.33 60.26 3631.27 9.93 98.68 598.62 -67.74 4588.71 -7.47 55.74 505.75 310.26 96261.27 15.93 253.89 4943.68 274.26 75218.55 6.63 44.01 1819.44 278.26 77428.63 12.63 159.62 3515.54 -167.74 28136.71 -12.57 157.90 2107.82 -120.74 14578.15 -5.47 29.88 659.96 -17.74 314.71 6.23 38.86 -110.59 -181.74 33029.43 -12.87 165.53 2338.27 -52.74 2781.51 -1.07 1.14 56.22 -102.74 10555.51 -5.77 33.25 592.40 -201.74 40699.03 -12.77 162.97 ...read more.

Conclusion

The book I used was printed in 2001, and although data this old may be ok for someone on a diet who only needs to know rough values, for my investigation I would have liked to have more accurate and up-to-date values. The other dilemma I met when collecting my data was that I was not really sure whether my data should be classed as elliptical or whether it was more of an exponential curve. I think I might have got a better correlation if I had decided to use a Spearman's Rank method as opposed to Pearson's Product Moment Correlation Coefficient. However, I decided that the best thing to do was to assume that the results were elliptical because they were close enough to being that way, but with only a couple of outliers towards the higher calorie and fat end. Overall, I think my investigation was quite accurate, but could have been more accurate using data to more decimal places, and using more decimal places in calculations. It might have been more interesting to try and use Spearman's Rank Order Correlation instead to see whether the results were similar, and if I were to repeat the investigation, and the results looked similar, it would certainly be something that I would consider. Josh Wakeford ...read more.

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