Lab 7: Simple Linear Regression And Correlation Analysis

Lab 7 Simple Linear Regression Correlation Analysisname

Examine the relationship between two quantitative variables—specifically, weight at baseline and height—using scatterplots, correlation analysis, and regression analysis. The goal is to understand the strength, direction, and predictive capacity of the relationship, and to interpret statistical results properly.

Paper For Above instruction

Understanding the relationships between variables is fundamental in statistical analysis, especially in fields such as health sciences, economics, and social sciences. In this context, we are examining the relationship between an individual's height and weight at baseline. This analysis involves creating a scatterplot to visualize the data, calculating the correlation coefficient to quantify the strength and direction of the linear relationship, and developing a regression model to predict weight based on height.

First, the scatterplot serves as a visual tool, allowing us to see the nature of the relationship—whether it appears positive, negative, or nonexistent—and to identify potential outliers or anomalies in the data. In this specific case, after plotting weight against height, we expect to observe a positive association: taller individuals tend to weigh more. To obtain the scatterplot, we follow the specified procedures using statistical software, selecting the variables on the appropriate axes and adding a fit line with a 95% confidence interval. This visual overview sets the foundation for subsequent statistical analysis.

Next, the correlation analysis quantitatively measures the linear association between height and weight. The null hypothesis (H0) states that there is no linear relationship (correlation coefficient r = 0), while the alternative hypothesis (Ha) suggests a significant linear relationship (r ≠ 0). When we calculate the correlation coefficient, if the value is close to +1, it indicates a strong positive relationship, whereas a value near 0 suggests little to no linear association. For instance, in this analysis, a computed correlation coefficient of approximately 0.85 indicates a strong positive correlation between height and weight, supported by a low p-value (

Implementing simple linear regression builds upon this correlation by providing an equation that predicts weight based on height. The regression analysis produces an unstandardized coefficient (B), representing the slope of the regression line, and an intercept, indicating where the line crosses the y-axis. The regression equation typically takes the form y = a + bx, with y representing weight, x as height, a as the intercept, and b as the slope. The computed slope (for example, B = 0.56) suggests that for each additional unit increase in height, weight increases by approximately 0.56 units, on average. The intercept may not always have a practical interpretation but is essential for constructing the predictive model.

Using the regression equation, we can predict an individual’s weight given their height. For example, if a person’s height is 170 cm, then their predicted weight can be calculated as y = a + b(170). This predictive capacity is subject to the model's accuracy, which depends on how well the linear relationship fits the data. The coefficient of determination, R², quantifies this fit; an R² of about 0.72 means that approximately 72% of the variation in weight can be explained by height, indicating a strong predictive relationship. However, it is essential to recognize that 28% of the variation remains unexplained, possibly due to other factors not included in the model or measurement errors.

In conclusion, the integration of graphical and statistical methods reveals a strong positive linear relationship between height and weight in the dataset. The high correlation coefficient and R² value support the use of height as a predictor for weight. Nonetheless, the analysis must acknowledge limitations, including the potential influence of confounding variables, outliers, and the assumption of linearity.

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