 Part 1a Coefficient of Variation = (Standard deviation /Mean) * 100 % Earlier Average weekly wages = 8 Mean = 8 Standard Deviation = 1 Coefficient of Variation = "(\\frac{1}{8})*100 = 12.5 \\%" After settlement, Average weekly wages = 12 Mean = 12 Standard Deviation = 1.5 Coefficient of Variation = "(\\frac{1.5}{12})*100 = 12.5 \\%" 12 > 8 Hence wages have become higher is Correct Coefficient of Variation is same hence no impact on the uniformity wages have become more uniform is not correct wages have become higher is Correct but more uniform is not correct Part 1b "\\bar{X}=\\dfrac{\\sum_iX_i}{n}=\\dfrac{70}{7}=10""\\bar{Y}=\\dfrac{\\sum_iY_i}{n}=\\dfrac{63}{7}=9""SS_{XX}=\\sum_i(X_i-\\bar{X})^2=\\sum_iX_i^2-n\\cdot\\bar{X}^2""=728-7(10)^2=28""SS_{YY}=\\sum_i(Y_i-\\bar{Y})^2=\\sum_iY_i^2-n\\cdot\\bar{Y}^2""=651-7(9)^2=84""SS_{XY}=\\sum_i(X_i-\\bar{X})(Y_i-\\bar{Y})=\\sum_iX_iY_i-n\\cdot\\bar{X}\\bar{Y}""=676-7(10)(9)=46""r=\\dfrac{SS_{XY}}{\\sqrt{SS_{XX}}\\sqrt{SS_{YY}}}=\\dfrac{46}{\\sqrt{28}\\sqrt{84}}\\approx""\\approx0.948504""0.7<r\\leq1" means a strong positive correlation. Part 1c The key distinction between correlation and regression is that the former evaluates the strength of a connection between two variables, let us say x and y. In this context, correlation is used to quantify degree, whereas regression is a metric used to determine how one variable influences another. Part 1d Regression coefficients are -2.7 and -0.3 The coefficient in regression with a single independent variable shows you how much the dependent variable is anticipated to grow (if the coefficient is positive) or decrease (if the coefficient is negative) when the independent variable increases by 2.7 and -0.3. The coefficient of correlation is 0.90 A correlation of -0.90, for example, implies the same degree of clustering as a correlation of +0.90. A positive correlation indicates that the cloud slopes upward; when one variable rises, the other rises as well. A negative correlation indicates that the cloud slopes downward; as one variable rise, the other falls. Solution: (a) Since the mean wage has increased, therefore, it is correct to say that mean wage has become higher, after settlement. In order to compare the uniformity of the wages before and after settlement, we have to compare their coefficient of variation. "\\begin{aligned}\n\nC V \\text { before settlement }= \\frac{1}{8} \\times 100=12.5 \\\\\n\nC V \\text { before settlement } =\\frac{1.5}{12} \\times 100=12.5\n\n\\end{aligned}" Since these coefficients are same, therefore, it is not correct to say that wages have become more uniform. (b) X Values: ∑ = 70 Mean = 10 ∑(X - Mx)2 = SSx = 28 Y Values: ∑ = 63 Mean = 9 ∑(Y - My)2 = SSy = 84 X and Y Combined: N = 7 ∑(X - Mx)(Y - My) = 46 R Calculation: r = ∑((X - My)(Y - Mx)) / "\\sqrt{(SSx)(SSy)}" r = 46 / "\\sqrt{(28)(84)}" = 0.9485 Interpretation: This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa). (c): The main difference in correlation vs regression is that the measures of the degree of a relationship between two variables; let them be x and y. Here, correlation is for the measurement of degree, whereas regression is a parameter to determine how one variable affects another. (d): Correlation coefficient is 0.90. Correlation between Xand Y variablesis high and positive. Y Dependent variable can predict the impact of independent variable X and other variable. High correlation value indicates less regression. R2 =( 0.90)2=0.81 R2 is a statistical measure of how close the data are to be fitted to regression line and whether the model is a good fit or not. R2 value is 0.81 is high. It indicates smaller differences between the oserved data fitted values. R2 of 0.81 means 81% of Variance in Y variable is predictable from the X variable. Regression coefficients are negative: -2.7 and -0.3. The proportion of variations between data VARIABLES is high.
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The two regression equations of the variables x and y are: x=19.13-0.87y y=11.64-0.50x Find: 1. mean of x's 2. mean of y's 3. correlation coefficient between x and y
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The two regression equations of the variables x and y are: x=19.13-0.87y y=11.64-0.50x Find: 1. mean of x's 2. mean of y's 3. correlation coefficient between x and y |
The two regression coefficients are -2.7 and -0.3 and the coefficient of correlation is 0.90 comment
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