Scatter Plots and Regression Analysis

What does a scatter plot show in business analysis?

• Trends over time

• Relationships between two variables

• Profit margins over several periods

• Employee satisfaction scores

In a scatter plot, a positive linear relationship between two variables indicates:

• When one variable increases, the other decreases.

• When one variable increases, the other also increases.

• There is no correlation between the two variables.

• Both variables remain constant over time.

What does it mean if points on a scatter plot are randomly distributed with no clear pattern?

• There is a strong positive correlation.

• There is no correlation between the variables.

• There is a strong negative correlation.

• The variables have a nonlinear relationship.

Which of the following best describes the role of a "trend line" in a scatter plot?

• It shows the average values of the variables.

• It represents the relationship between the variables.

• It identifies outliers in the dataset.

• It calculates the median of the dataset.

In a business context, what might a scatter plot of advertising spend and sales show?

• If increased advertising leads to higher sales

• If the company is losing money

• Whether customers are satisfied

• The total number of products sold

In a simple linear regression model, what is the purpose of the "regression line"?

• To display actual data points

• To predict the dependent variable based on the independent variable

• To show the average value of the dependent variable

• To calculate standard deviation

Which of the following metrics indicates how well a regression model fits the data?

• Mean

• Standard Deviation

• R-squared

• Median

What does an R-squared value of 0.90 mean in a business regression model?

• 90% of the variability in the independent variable is explained by the dependent variable.

• 90% of the variability in the dependent variable is explained by the independent variable.

• The independent variable is not a significant predictor.

• The model is incorrect.

In a business regression model, a low p-value (e.g., < 0.05) indicates:

• The independent variable has a statistically significant effect on the dependent variable.

• The regression model does not fit the data well.

• There is no relationship between the variables.

• The model is overfitting the data.

Which of the following best describes multicollinearity in multiple regression analysis?

• All independent variables are highly correlated with each other.

• The dependent variable cannot be predicted by any independent variable.

• The regression model has too many observations.

• The independent variables have no relationship with the dependent variable.