Final Project Regression and Correlation Analysis

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Oxford University *

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770B

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Biology

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Nov 24, 2024

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Uploaded by emmanuelngetich35

1 Final Project Student Name University Affiliation Professor Date of Submission

2 Regression and Correlation Analysis Step 1: Scatterplot for the specified dependent variable (Y) and the selected independent variable (X) with the graph of the "best fit" 40 45 50 55 60 65 70 75 150 155 160 165 170 175 180 185 f(x) = 0.54 x + 141.18 R² = 0.45 Step 2: The equation of the "best fit" line y = 0.5351x + 141.18 Step 3: The coefficient of correlation The correlation coefficient is a relationship measure between the comparative movements of two variables (Puniya & Sing, 2019). Its values range between -1.0 and 1.0, a correlation of -1.0 indicates a perfect negative correlation, whereas 1.0 indicates a perfect positive correlation, and a correlation of 0.0 indicates no linear relationship between variables. Therefore, the coefficient of correlation (r) is 0.669

3 Step 4: Coefficient of Determination The coefficient of determination (r 2 ) is 0.4481 Step 5: Utility of the regression model One-Tailed Test: H(o): B(β1) = 0, H(a): B(β1) <0 Two-Tailed Test: H(o): B(β1) = 0, H(a): B(β1) ≠ 0 Rejection region: t < -t α or |t| > t α/2 tc =-1.661 and tc=1.661 or t=|1.96| when n-2=48 and α=0.10 n-2=48 represent the degrees of freedom The P-Value is 1.45E-07 The result is significant at p < .10 Step 6: Ability of the independent variable to predict the dependent variable Linear regression predicts an unknown variable's value from another variable's known value. When X and Y are two related variables, linear regression helps predict Y for a given value of X and vice versa (Lemenkova, 2019). We indicate models with one independent and one dependent variable; the known predicted value is the dependent variable, while the unknown predicted value is the independent variable. The equation would be Y = a + bX Step 7: Confidence interval using a 95% confidence interval The 95% confidence interval for weight is 1.6396 Hence; 58.2857 ± 1.6396

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4 The 95% confidence interval for height is 1.3106 Hence; 172.3673 ± 1.3106 Step 8: 99% confidence interval for the dependent variable for the selected value of an independent variable. M = 58.29, 99% CI M = 58.29 t = 2.58 SM = √ (12/100) = 0.1 μ = M ± Z(sM) μ = 58.29 ± 2.58 * 0.1 μ = 58.29 ± 0.258 Step 9: M = 172.37, 99% CI M = 172.37 t = 2.58 SM = √ (12/100) = 0.1 μ = M ± Z(sM) μ = 172.37 ± 2.58 * 0.1 μ = 172.37 ± 0.258

5 Step 10: A positive slope value indicates a positive relationship between the dependent and independent variables; hence as the independent variable increases, the dependent variable also increases Step 11: Correlation is applied in businesses to outline the relationship between various data sets in business and is also involved in financial analysis and to support the decision-making process. Research can be used in predicting future market trends. It helps business leaders make predictions based on patterns in their data and helps guide business processes, performance, and direction of trends.

6 References Lemenkova, P. (2019). Testing linear regressions by StatsModel Library of Python for oceanological data interpretation. Aquatic Sciences and Engineering , 34 (2), 51-60. Puniya, M., & Sing, R. B. (2019). Correlation and regression analysis. Int J Res Eng Sci Manage , 2 , 456-8. Schober, P., Boer, C., & Schwarte, L. A. (2018). Correlation coefficients: appropriate use and interpretation. Anesthesia & analgesia , 126 (5), 1763-1768.

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