Multiple Regression and Correlation Analysis †MyAssignmenthelp.com

Question: Discuss about the Multiple Regression and Correlation Analysis. Answer: Introduction: Simple Random sampling has been used data in selecting a sample. The sampling is a representation of the population in a way that every respondent/ individual has an equal probability to be chosen (Mertens 2014). Also, it is easy to select and is done using random selection or through random number. It has been used in collection because free from errors, bias and prejudice, with only minimum knowledge and easily used especially for data analysis using inferential statistics. Also, the sampling error in this method can be easily calculated. Alcohol Meals Fuel Phone Mean 1227.36 1551.29 2128.02 1452.15 Median 891 960 1440 1200 Mode 0 0 1200 1200 Standard Deviation 1484.298 3703.566 2246.358 1362.19 Sample Variance 2203142 13716399 5046123 1855561 Standard Error 104.9557 261.8816 158.8415 96.32135 Range 10428 48000 18000 9600 Skewness 2.185617 10.41627 3.337669 3.120751 Kurtosis 7.75614 126.6637 16.93805 12.38359 Table 1b: Descriptive Statistics of Alcohol, Fuel, Meals and Phone The method of variation that can be appropriately used in this case for analysis is standard deviation. It is often believed to be an easy method as it helps in describing the sample that is clustered around the mean in a set of given data (Schabenberger Gotway, 2017. Also, when the variables analysed are spread apart then they are supposedly mean to have a high standard deviation. In addition, the data, meals has the maximum standard deviation as it 3703 AUD away from the means of 1551. The same thing can be explained in case full which often experiences much fluctuation during a normal course of time. On the contrary, it can be said less the deviation, less would be fluctuation/ changes of the expenditure and the other way around. The box plot just like normal distribution is a method of depicting variation using method of variation as quartile. The figure 1b shows fluctuation / changes and the maximum has been shown by the expenditure on meals, fuels, alcohol and then phone. Moreover, the annual expenditure distribution of data is higher in upper quartile than in low quartile range (Hinton, 2014). Comparatively as per the descriptive statistics, meals, fuels, alcohol and phone have variation as mean medina mode depicting positive skewness. However, the maximum deviation is in meals followed by other like fuels, alcohol and phone. Classes Frequency Percentage Cumm Percentage 0-400 19 9.50% 9.50% 400-800 45 22.50% 32.00% 800-1200 56 28.00% 60.00% 1200-1600 33 16.50% 76.50% 1600-2000 26 13.00% 89.50% 2000-2400 11 5.50% 95.00% 2400-2800 3 1.50% 96.50% 2800-3200 3 1.50% 98.00% More than 3200 4 2.00% 100.00% Table 2a: Frequency distribution of the variableUtilities The percentages of household spend on utilities can be given as: 1a. i. At most AUD $1200 per annum on utilities = 56/ 200 = 28% 1a. ii. Between AUD $1200 per annum and AUD $2400 per annum on utilities= (16.5 + 13 + 5.5) percent = 35% 1a. iii. more than AUD $2400 per annum on utilities = (1.5 + 1.5 + 2) percent = 5% The interpretation can be done in two different ways. First is mathematically, where mean, medina and mode are there to analyse the situation followed by histograms shape and size. As per mathematical distribution, a normal distribution has mean, mode and median all as equal (Manley Alberto, 2016). Whereas, in this case as per the table 2c given below; mean, mode and median are not at all equal showing discrepancy. This depicts that the data is slightly bend towards one side that is right side of the mean. In contrast, this household data on annual expenditure on utilities is given as: Mean of Utilities 1220 Median of Utilities 1100 Mode of Utilities 1000 Table 2c: Mathematical Interpretation on Utilities Hence, Mean median = mode, a positive bend whether the shape and size of the histogram below is majorly shows a high on expenditure from 800-1200 AUD. However, in histogram the data is on the left side depicting positive skewness (Corder Foreman, 2014). The percentiles are gathered to analyse the group with their values. However, lower 10% is 10th percentile and upper 10% is 90th percentiles which are AUD 18351.2 and AUD 107760.4 respectively. The ownhouse variable is to analyse the actual residents based on the expenditure. This variable is given by values 0 and 1 where 1 is the ones that own a house and 0 who doesnt. As per the data of 200 samples, the numbers of household that have their own houses are 141. However, mean is 141/200 which is 0.07 Mean of own house = 135/ 200 = 0.68 As per the average implies, there are more than average number of households that own a house. Family size is calculated by adding adults and children together. However, the total family size of 5 comes out to be 14. It has been calculated using the COUNTIF function in excel. The probability of family size as 5 is given as: Probability of Family size =5 = 14/200 = 0.070 The scatter plot for log of (texp) againstlog of (ataxinc) is very well shown in figure 3d. The plots shows a growing trend in the annual expenditure is growing against after tax annual income. However, this indicates a growing demand of the resources like alcohol, meals, fuels, etc. On the other hand, the correlation comes out to be 0.978187 shows they have strong relationship. This positive correlation further emphasizes the effect that they may have on each other in terms of expenditure (Cohen et al., 2013). Values Row Labels Count of Highest Degree Count of GHH F 100 100 B 22 22 I 25 25 M 14 14 P 19 19 S 20 20 M 100 100 B 22 22 I 22 22 M 21 21 P 12 12 S 23 23 Grand Total 200 200 The frequency table explains that the count of males and females in the same is qual that is 100 each. However, as per the distribution based on level of education; the males as well as females have equal number of people having Bachelors degree. However, higher level of education accompany Bachelors degree and Masters, the number differ at the Masters degree. While females constitutes to have 14 people having Masters Degree whereas males constitutes to have 14 people having Masters Degree, which is more than females higher level of education at any case. On the contrary, the male and females heads have a difference in their level of qualification. Female Male Total Bachelor 0.110 0.110 0.220 Intermediate 0.125 0.110 0.235 Master 0.070 0.105 0.175 Primary 0.095 0.060 0.155 Secondary 0.100 0.115 0.215 Total 0.500 0.500 1.000 Probability of (Head of household = Male and Level of Education = Bachelor Degree) (Male as HH and Bachelors Degree as Level of Education / Total) 22/200 = 0.110 11% U = Probability of being Gender as Male 100/200 = 0.65 50% V = Probability of Level of Education as Masters Degree 35/200 = 0.175 17.5% Pr (U) * Pr (V) 0.65*0.175 = 0.0875 8.75% Pr (UV) 21/200 = 0.105 10.5% However, as depicted through step by step method Pr (U) * Pr (V) is not equal to Pr (UV) depicting that the two variables Gender = Male and Level of Education = Masters Degree are not independent. This is because their probabilities do not match; if they could have been same then that illustrates one is related to the other (rather being dependent) and not independent in nature. References Cohen, J., Cohen, P., West, S. G., Aiken, L. S. (2013).Applied multiple regression/correlation analysis for the behavioral sciences. Routledge. Corder, G. W., Foreman, D. I. (2014).Nonparametric statistics: A step-by-step approach. John Wiley Sons. Hinton, P. R. (2014).Statistics explained. Routledge. Mertens, D. M. (2014).Research and evaluation in education and psychology: Integrating diversity with quantitative, qualitative, and mixed methods. Sage publications. Schabenberger, O., Gotway, C. A. (2017).Statistical methods for spatial data analysis. CRC press.