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**Parts I–II:** Review and revise your individual project from last week. Then, add the following responses to your document:

**Part III: Regression and Correlation**

Based on what you have learned from your research on regression analysis and correlation, answer the following questions about the Body Fat Versus Weight data set:

- When performing a regression analysis, it is important to first identify your independent/predictor variable versus your dependent/response variable, or simply put, your
*x*versus*y*variables. How do you decide which variable is your predictor variable and which is your response variable? - Based on the Body Fat Versus Weight data set, which variable is the predictor variable? Which variable is the response variable? Explain.
- Using Excel, construct a scatter plot of your data. – DONE
- Using the graph and intuition, determine whether there is a positive correlation, a negative correlation, or no correlation. How did you come to this conclusion?
- Calculate the correlation coefficient,
*r*, and verify your conclusion with your scatter plot. What does the correlation coefficient determine? Discuss the strength of the correlation coefficient calculated, and if the correlation is positive or negative. - Add a regression line to your scatter plot, and obtain the regression equation.
- Does the line appear to be a good fit for the data? Why or why not?

- Regression equations help you make predictions. Using your regression equation, discuss what the slope means, and determine the predicted value of weight when body fat is zero. Interpret the meaning of this result.

**Part IV: Putting it Together**

Your analysis is now complete, and you are ready to report your findings to your boss. In one paragraph, summarize your results by explaining your findings from the statistical measures, hypothesis test, and regression analysis of body fat and weight for the 252 men attending Silver’s Gym.

I have attached the completed Excel spreadsheet, and also the Word document that needs to be modified per the instructor’s suggestions. Please contact me with any questions. Thank you.

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Attachment

IDNO | BODYFAT | WEIGHT | ||||||||||

1 | 12.6 | 154.25 | Description: | The dataset provided here is based on a sample of 252 men. | ||||||||

2 | 6.9 | 173.25 | Their body fat and weights were recorded. | |||||||||

3 | 24.6 | 154.00 | ||||||||||

4 | 10.9 | 184.75 | Statement: | The doctors office claims that the mean body fat in men is 20%. | ||||||||

5 | 27.8 | 184.25 | ||||||||||

6 | 20.6 | 210.25 | Source: http://www2.stetson.edu/~jrasp/data.htm | |||||||||

7 | 19.0 | 181.00 | Body Fat (%) | Body Weight (Pounds) | ||||||||

8 | 12.8 | 176.00 | Mean | 18.9 | 178.92 | |||||||

9 | 5.1 | 191.00 | ||||||||||

10 | 12.0 | 198.25 | Median | 19.0 | 176.50 | |||||||

11 | 7.5 | 186.25 | ||||||||||

12 | 8.5 | 216.00 | Range | 45.1 | 244.65 | |||||||

13 | 20.5 | 180.50 | ||||||||||

14 | 20.8 | 205.25 | Standard | 7.750856 | 29.38916 | |||||||

15 | 21.7 | 187.75 | Deviation | |||||||||

16 | 20.5 | 162.75 | ||||||||||

17 | 28.1 | 195.75 | Part 2: Hypothesis Test Calculation | |||||||||

18 | 22.4 | 209.25 | ||||||||||

19 | 16.1 | 183.75 | Population Mean of Body Fat | 20 | ||||||||

20 | 16.5 | 211.75 | ||||||||||

21 | 19.0 | 179.00 | Standard Deviation of Body Fat | 7.750856 | ||||||||

22 | 15.3 | 200.50 | ||||||||||

23 | 15.7 | 140.25 | Cumulative Probablity | 0.98515 | ||||||||

24 | 17.6 | 148.75 | (Calculated) | |||||||||

25 | 14.2 | 151.25 | ||||||||||

26 | 4.6 | 159.25 | P-Value on Right Tail | 0.01485 | ||||||||

27 | 8.5 | 131.50 | ||||||||||

28 | 22.4 | 148.00 | P-Value for Two Tails | 0.0297 | ||||||||

29 | 4.7 | 133.25 | ||||||||||

30 | 9.4 | 160.75 | ||||||||||

31 | 12.3 | 182.00 | ||||||||||

32 | 6.5 | 160.25 | ||||||||||

33 | 13.4 | 168.00 | ||||||||||

34 | 20.9 | 218.50 | ||||||||||

35 | 31.1 | 247.25 | ||||||||||

36 | 38.2 | 191.75 | ||||||||||

37 | 23.6 | 202.25 | ||||||||||

38 | 27.5 | 196.75 | ||||||||||

39 | 33.8 | 363.15 | ||||||||||

40 | 31.3 | 203.00 | ||||||||||

41 | 33.1 | 262.75 | ||||||||||

42 | 31.7 | 205.00 | ||||||||||

43 | 30.4 | 217.00 | ||||||||||

44 | 30.8 | 212.00 | ||||||||||

45 | 8.4 | 125.25 | ||||||||||

46 | 14.1 | 164.25 | ||||||||||

47 | 11.2 | 133.50 | ||||||||||

48 | 6.4 | 148.50 | ||||||||||

49 | 13.4 | 135.75 | ||||||||||

50 | 5.0 | 127.50 | ||||||||||

51 | 10.7 | 158.25 | ||||||||||

52 | 7.4 | 139.25 | ||||||||||

53 | 8.7 | 137.25 | ||||||||||

54 | 7.1 | 152.75 | ||||||||||

55 | 4.9 | 136.25 | ||||||||||

56 | 22.2 | 198.00 | ||||||||||

57 | 20.1 | 181.50 | ||||||||||

58 | 27.1 | 201.25 | ||||||||||

59 | 30.4 | 202.50 | ||||||||||

60 | 24.0 | 179.75 | ||||||||||

61 | 25.4 | 216.00 | ||||||||||

62 | 28.8 | 178.75 | ||||||||||

63 | 29.6 | 193.25 | ||||||||||

64 | 25.1 | 178.00 | ||||||||||

65 | 31.0 | 205.50 | ||||||||||

66 | 28.9 | 183.50 | ||||||||||

67 | 21.1 | 151.50 | ||||||||||

68 | 14.0 | 154.75 | ||||||||||

69 | 7.1 | 155.25 | ||||||||||

70 | 13.2 | 156.75 | ||||||||||

71 | 23.7 | 167.50 | ||||||||||

72 | 9.4 | 146.75 | ||||||||||

73 | 9.1 | 160.75 | ||||||||||

74 | 13.7 | 125.00 | ||||||||||

75 | 12.0 | 143.00 | ||||||||||

76 | 18.3 | 148.25 | ||||||||||

77 | 9.2 | 162.50 | ||||||||||

78 | 21.7 | 177.75 | ||||||||||

79 | 21.1 | 161.25 | ||||||||||

80 | 18.6 | 171.25 | ||||||||||

81 | 30.2 | 163.75 | ||||||||||

82 | 26.0 | 150.25 | ||||||||||

83 | 18.2 | 190.25 | ||||||||||

84 | 26.2 | 170.75 | ||||||||||

85 | 26.1 | 168.00 | ||||||||||

86 | 25.8 | 167.00 | ||||||||||

87 | 15.0 | 157.75 | ||||||||||

88 | 22.6 | 160.00 | ||||||||||

89 | 8.8 | 176.75 | ||||||||||

90 | 14.3 | 176.00 | ||||||||||

91 | 20.2 | 177.00 | ||||||||||

92 | 18.1 | 179.75 | ||||||||||

93 | 9.2 | 165.25 | ||||||||||

94 | 24.2 | 192.50 | ||||||||||

95 | 9.6 | 184.25 | ||||||||||

96 | 17.3 | 224.50 | ||||||||||

97 | 10.1 | 188.75 | ||||||||||

98 | 11.1 | 162.50 | ||||||||||

99 | 17.7 | 156.50 | ||||||||||

100 | 21.7 | 197.00 | ||||||||||

101 | 20.8 | 198.50 | ||||||||||

102 | 20.1 | 173.75 | ||||||||||

103 | 19.8 | 172.75 | ||||||||||

104 | 21.9 | 196.75 | ||||||||||

105 | 24.7 | 177.00 | ||||||||||

106 | 17.8 | 165.50 | ||||||||||

107 | 19.1 | 200.25 | ||||||||||

108 | 18.2 | 203.25 | ||||||||||

109 | 17.2 | 194.00 | ||||||||||

110 | 21.0 | 168.50 | ||||||||||

111 | 19.5 | 170.75 | ||||||||||

112 | 27.1 | 183.25 | ||||||||||

113 | 21.6 | 178.25 | ||||||||||

114 | 20.9 | 163.00 | ||||||||||

115 | 25.9 | 175.25 | ||||||||||

116 | 16.7 | 158.00 | ||||||||||

117 | 19.8 | 177.25 | ||||||||||

118 | 14.1 | 179.00 | ||||||||||

119 | 25.1 | 191.00 | ||||||||||

120 | 17.9 | 187.50 | ||||||||||

121 | 27.0 | 206.50 | ||||||||||

122 | 24.6 | 185.25 | ||||||||||

123 | 14.8 | 160.25 | ||||||||||

124 | 16.0 | 151.50 | ||||||||||

125 | 14.0 | 161.00 | ||||||||||

126 | 17.4 | 167.00 | ||||||||||

127 | 26.4 | 177.50 | ||||||||||

128 | 17.4 | 152.25 | ||||||||||

129 | 20.4 | 192.25 | ||||||||||

130 | 15.0 | 165.25 | ||||||||||

131 | 18.0 | 171.75 | ||||||||||

132 | 22.2 | 171.25 | ||||||||||

133 | 23.1 | 197.00 | ||||||||||

134 | 25.3 | 157.00 | ||||||||||

135 | 23.8 | 168.25 | ||||||||||

136 | 26.3 | 186.00 | ||||||||||

137 | 21.4 | 166.75 | ||||||||||

138 | 28.4 | 187.75 | ||||||||||

139 | 21.8 | 168.25 | ||||||||||

140 | 20.1 | 212.75 | ||||||||||

141 | 24.3 | 176.75 | ||||||||||

142 | 18.1 | 173.25 | ||||||||||

143 | 22.7 | 167.00 | ||||||||||

144 | 9.9 | 159.75 | ||||||||||

145 | 10.8 | 188.15 | ||||||||||

146 | 14.4 | 156.00 | ||||||||||

147 | 19.0 | 208.50 | ||||||||||

148 | 28.6 | 206.50 | ||||||||||

149 | 6.1 | 143.75 | ||||||||||

150 | 24.5 | 223.00 | ||||||||||

151 | 9.9 | 152.25 | ||||||||||

152 | 19.1 | 241.75 | ||||||||||

153 | 10.6 | 146.00 | ||||||||||

154 | 16.5 | 156.75 | ||||||||||

155 | 20.5 | 200.25 | ||||||||||

156 | 17.2 | 171.50 | ||||||||||

157 | 30.1 | 205.75 | ||||||||||

158 | 10.5 | 182.50 | ||||||||||

159 | 12.8 | 136.50 | ||||||||||

160 | 22.0 | 177.25 | ||||||||||

161 | 9.9 | 151.25 | ||||||||||

162 | 14.8 | 196.00 | ||||||||||

163 | 13.3 | 184.25 | ||||||||||

164 | 15.2 | 140.00 | ||||||||||

165 | 26.5 | 218.75 | ||||||||||

166 | 19.0 | 217.00 | ||||||||||

167 | 21.4 | 166.25 | ||||||||||

168 | 20.0 | 224.75 | ||||||||||

169 | 34.7 | 228.25 | ||||||||||

170 | 16.5 | 172.75 | ||||||||||

171 | 4.1 | 152.25 | ||||||||||

172 | 1.9 | 125.75 | ||||||||||

173 | 20.2 | 177.25 | ||||||||||

174 | 16.8 | 176.25 | ||||||||||

175 | 24.6 | 226.75 | ||||||||||

176 | 10.4 | 145.25 | ||||||||||

177 | 13.4 | 151.00 | ||||||||||

178 | 28.8 | 241.25 | ||||||||||

179 | 22.0 | 187.25 | ||||||||||

180 | 16.8 | 234.75 | ||||||||||

181 | 25.8 | 219.25 | ||||||||||

182 | 0.0 | 118.50 | ||||||||||

183 | 11.9 | 145.75 | ||||||||||

184 | 12.4 | 159.25 | ||||||||||

185 | 17.4 | 170.50 | ||||||||||

186 | 9.2 | 167.50 | ||||||||||

187 | 23.0 | 232.75 | ||||||||||

188 | 20.1 | 210.50 | ||||||||||

189 | 20.2 | 202.25 | ||||||||||

190 | 23.8 | 185.00 | ||||||||||

191 | 11.8 | 153.00 | ||||||||||

192 | 36.5 | 244.25 | ||||||||||

193 | 16.0 | 193.50 | ||||||||||

194 | 24.0 | 224.75 | ||||||||||

195 | 22.3 | 162.75 | ||||||||||

196 | 24.8 | 180.00 | ||||||||||

197 | 21.5 | 156.25 | ||||||||||

198 | 17.6 | 168.00 | ||||||||||

199 | 7.3 | 167.25 | ||||||||||

200 | 22.6 | 170.75 | ||||||||||

201 | 12.5 | 178.25 | ||||||||||

202 | 21.7 | 150.00 | ||||||||||

203 | 27.7 | 200.50 | ||||||||||

204 | 6.8 | 184.00 | ||||||||||

205 | 33.4 | 223.00 | ||||||||||

206 | 16.6 | 208.75 | ||||||||||

207 | 31.7 | 166.00 | ||||||||||

208 | 31.5 | 195.00 | ||||||||||

209 | 10.1 | 160.50 | ||||||||||

210 | 11.3 | 159.75 | ||||||||||

211 | 7.8 | 140.50 | ||||||||||

212 | 26.4 | 216.25 | ||||||||||

213 | 19.3 | 168.25 | ||||||||||

214 | 18.5 | 194.75 | ||||||||||

215 | 19.3 | 172.75 | ||||||||||

216 | 45.1 | 219.00 | ||||||||||

217 | 13.8 | 149.25 | ||||||||||

218 | 8.2 | 154.50 | ||||||||||

219 | 23.9 | 199.25 | ||||||||||

220 | 15.1 | 154.50 | ||||||||||

221 | 12.7 | 153.25 | ||||||||||

222 | 25.3 | 230.00 | ||||||||||

223 | 11.9 | 161.75 | ||||||||||

224 | 6.1 | 142.25 | ||||||||||

225 | 11.3 | 179.75 | ||||||||||

226 | 12.8 | 126.50 | ||||||||||

227 | 14.9 | 169.50 | ||||||||||

228 | 24.5 | 198.50 | ||||||||||

229 | 15.0 | 174.50 | ||||||||||

230 | 16.9 | 167.75 | ||||||||||

231 | 11.1 | 147.75 | ||||||||||

232 | 16.1 | 182.25 | ||||||||||

233 | 15.5 | 175.50 | ||||||||||

234 | 25.9 | 161.75 | ||||||||||

235 | 25.5 | 157.75 | ||||||||||

236 | 18.4 | 168.75 | ||||||||||

237 | 24.0 | 191.50 | ||||||||||

238 | 26.4 | 219.15 | ||||||||||

239 | 12.7 | 155.25 | ||||||||||

240 | 28.8 | 189.75 | ||||||||||

241 | 17.0 | 127.50 | ||||||||||

242 | 33.6 | 224.50 | ||||||||||

243 | 29.3 | 234.25 | ||||||||||

244 | 31.4 | 227.75 | ||||||||||

245 | 28.1 | 199.50 | ||||||||||

246 | 15.3 | 155.50 | ||||||||||

247 | 29.1 | 215.50 | ||||||||||

248 | 11.5 | 134.25 | ||||||||||

249 | 32.3 | 201.00 | ||||||||||

250 | 28.3 | 186.75 | ||||||||||

251 | 25.3 | 190.75 | ||||||||||

252 | 30.7 | 207.50 |

Improvements that need to be made to this.

Opportunities for improvement: Notice that your EXCEL calculations are correct. Inside your word document, you did not actually use the calculated results in Sheet 1 to interpret some of the results. You were asked to compare the ratio of the average body fat to average body weight to that of the Gym manager’s claim. Also, you were suggested to compare the calculated mean and median to make a statement about the shape of the distribution. In second part, you discussed about using Chi Square Test while I clearly stated to use the Z-Test. Chi Square test is mainly used when the test is about a qualitative or categorical variable. Also, you did not state the five steps of hypothesis test the way shown during the live chat and posted inside its power point presentation. You did not state the hypotheses and your conclusion is incorrect.

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** **

** **

** **

** **

**Part 1 **

Central tendency is a typical or central value for a probability distribution. It is sometimes referred to as the center or average of distribution. Commonly used measures of central tendency in statistical analysis are arithmetic median, mode and mean. Average or center value for body weight and body weight can be calculated using mean, mode and range(Kuehl, & Kuehl, 2000).

**Arithmetic mean**

Arithmetic mean is simply known as the mean or average. Mean is calculated by summing up all numbers in a data collection then dividing the sum by total count of numbers in the collection. The collection is a set of results from a survey or an experiment. Mean is normally affected by outliers (outliers are values that are too small or too large compared to others). The mean for body weight and body fat was calculated by summing up all the values then dividing the by 252. Mean for body weight is 178.92 while that of body fat is 18.9.The result shows that average for body weight is 178.92 while the average for body fat is 18.9. Mean is important because it gives the average which can be used for comparison purposes. Mean also gives summary of the whole data by availing one value that describes the data. Mean is more applicable for this survey than the median because it summarizes the whole data (Dixon, & Massey, 2009).

**Median**

Median is value divides the upper half and lower half of probability distribution, population or data samples. Median can be gotten by arranging all the numbers from lower value to the highest value and then picking the value that falls in the middle. Median can help determine measure of location especially when there is skew in the distribution. Median is not affected by outliers in the data. The median for body fat was found to be 19 while that for body weight was 178.92. The value 19 is the middle value body fat and it divides the value into two, that is, it divides the highest and lowest values of body fat. The value 178.92 also falls in the middle of body weight’s data (Kuehl, & Kuehl, 2000).

**Range **

Range is difference calculated between smallest value and largest value. Range provides a sign of statistical dispersion. It is important in giving dispersion of small data collection. Range for the body fat was calculated by getting the difference between the highest and lowest values, same as the body weight. The calculated range for body fat is 45.1 while range for body weight is 244.65. These values show the level of dispersion in body fat and body weight. Range is important in statistics because it shows how the data sets have spread.

**Standard deviation **

** **Standard deviation (SD) is used in statistics to measure dispersion or amount of variation from the average. A high SD shows the how the data points have spread over a range of values while low SD shows how the data sets are close to the mean. Without SD it is difficult to determine if values are closer to the mean. Body fat had SD of 7.75 while body weight had standard deviation of 29.39. The standard deviation calculated shows that data sets are widely dispersed from the mean.

**Part 2**

The hypothesis was tested using chi-square that generated the p-value. According to chi-square, hypothesis is accepted if the calculated p-value falls within thresh hold values. The test was not statistically significant so we accept the null hypothesis and reject the alternate hypothesis. We are to accept the hypothesis that average body fat of men attending Silver Gym is 20%. Null hypothesis is accepted because both calculate p-values are below the thresh hold value of 0.05(Sincich, 2003).

**Reference**

Sincich, T. (2003). *A second course in statistics: regression analysis*. Upper Saddle River, New Jersey: Pearson Education, Inc.

Kuehl, R. O., & Kuehl, R. O. (2000). Design of experiments: statistical principles of research design and analysis.

Dixon, W. J., & Massey, F. J. (2009). *Introduction to statistical analysis* (Vol. 344). New York: McGraw-Hill.