University:
Washington State University
Course:
MATH 172 | Calculus II
Academic year:

2024
Views:

457

Pages:

5
Author:

Bailey Ayala

Question 1 Name one data shape different from symmetric and right/left-skewed. Name four graphs that summarize data. Answer: Data shape different from symmetric and right/left-skewed: Bimodal. Four graphs that summarize data: Box Plot Bar Chart Histogram Scatterplot Question 2 Multiple Linear Regression Assumptions: a. The distribution of possible values of the response variable corresponding to predictor variables 𝑥 1 x 1 and 𝑥 2 x 2 is called the distribution of the response variable. b. Four assumptions of multiple linear regression inferences: Linearity: A linear relationship exists between the predictor variables and the dependent variable. Normality: Residuals (differences between observed and predicted values) are normally distributed. Multicollinearity: Predictor variables should not be highly correlated with each other. Homoscedasticity: Variance of residuals should be constant across the range of predictor variables. Question 3 Which scatterplots have the most positive correlation and closer to zero correlation? Answer: Most positive correlation: Scatterplot B. The points show a clear upward trend as 𝑥 x-values increase. Closer to zero correlation: Scatterplot D. The points appear random with no discernible pattern. Question 4 Unusual Points in Scatterplots: Residuals and leverage: Residual: Difference between the observed value and predicted value. Leverage: Points far from the mean of 𝑥 x-values have high leverage, pulling the regression line toward them. Influential point: A point is influential if removing it significantly changes the regression line or correlation. Analysis of scatterplots (a–d): a. The point has high leverage and a high residual. It is an influential point as removing it weakens the correlation. Removing it increases the slope of the regression line. b. The point has high leverage but small residual. It is an influential point. Removing it weakens the association. Removing it increases the slope toward zero. c. The point has low leverage and moderate residual. It is not an influential point. Removing it slightly reinforces the correlation without affecting the slope. d. The point has high leverage and small residual. It supports the negative association. Removing it weakens the association. Removing it does not significantly change the slope.