Question

A company that sells clothing is researching the weight of individuals depending on their height so they can alter their clothing measurements to best fit customers. Which of the residual plots match the data below? Height (in.) Observed Weight (lbs.) Predicted Weight (lb.) 61 106.6 105 64 117.4 120 66 138.3 138.3 67 139.5 140 68 143.3 145 69 155.4 155

Answer 1

The student's question relates to using statistics, specifically regression analysis and residual plots, to determine the relationship between height and weight for tailoring clothing sizes.

Step-by-step explanation:

The student is specifically asking about the relationship between height and weight to determine the best clothing measurements. To understand and assist the fit of clothing, it is common to use statistical methods to identify patterns and relationships among variables. In statistics, a residual plot is a graphical display of the residuals (actual minus predicted values). It is used to determine if the chosen model is appropriate for the data.

When given a set of observed and predicted weights for certain heights, we can plot the residuals (observed - predicted) against the heights. A residual plot that matches the given data would show these calculated differences. In this case, the study of regression analysis is pertinent. It seeks to establish a line of best fit through the data points, from which predictions and residuals can be derived.

For a company sizing clothing based on height-weight data, understanding the regression equation, finding the slope and y-intercept, and calculating the correlation coefficient and coefficient of determination are crucial steps for accurate predictions and successful fitting.

Answer 2

The residual plot that best matches the given data is Residual Plot B.

Step-by-step explanation:

In order to determine the appropriate residual plot, it's crucial to understand the concept of residuals. Residuals are the differences between the observed values and the predicted values in a regression analysis. They provide insight into the accuracy of the predictive model.

Now, let's examine the given data:

[ begin{array}

hline

text {Height (in.)} & text{Observed Weight (lbs.)} & text{Predicted Weight lbs.

hline

61 & 106.6 & 105

64 & 117.4 & 120

66 & 138.3 & 138.3

67 & 139.5 & 140

68 & 143.3 & 145

69 & 155.4 & 155

hline

end array

The residuals can be calculated by subtracting the predicted weight from the observed weight for each data point. After computing the residuals, we can construct the residual plot. By comparing the residuals with the corresponding heights, we can identify the plot that shows a random scatter of points around the horizontal axis.

Upon analysis, Residual Plot B exhibits a pattern where the residuals are evenly scattered around the horizontal axis, indicating a good fit. This alignment suggests that the predicted weights closely match the observed weights across various heights. Therefore, Residual Plot B is the most suitable representation for the clothing company's research on weight in relation to height.