quiz 3 Flashcards
What is a Point Estimate?
Single value estimate of a population parameter (e.g., sample mean)
Point estimates provide a specific value as an estimate for a population characteristic.
What is an Interval Estimate?
Range within which the parameter is expected to lie with a certain confidence level
Interval estimates give a range instead of a single value, reflecting uncertainty.
What is the formula for Confidence Intervals (CI)?
CI = x̄ ± (critical value) × standard error
The critical value depends on the chosen confidence level and the distribution used.
When should you use z-distribution?
When the population standard deviation is known
Z-distribution is used for large samples or known population parameters.
When should you use t-distribution?
When the population standard deviation is unknown
T-distribution is more appropriate for smaller samples.
What does a 95% CI indicate?
There’s a 95% chance the interval contains the true population parameter
Confidence intervals provide a range of values that likely contain the population parameter.
What is the Standard Error (SE) of the mean when population SD is known?
SE of the mean = σ/n
SE measures the dispersion of the sample mean estimate from the true population mean.
What is the Standard Error (SE) of the mean when population SD is unknown?
SE of the mean = s/n
The sample standard deviation (s) is used in place of the population standard deviation.
What are the first two steps in Hypothesis Testing?
Define null (H0) and alternative (H1) hypotheses; Choose significance level α (commonly 0.05)
These steps establish the framework for testing the hypothesis.
What is the purpose of computing a test statistic in hypothesis testing?
To compare against critical value or p-value
The test statistic helps determine whether to reject or fail to reject the null hypothesis.
What does it mean to reject H0?
Conclude that there is sufficient evidence to support H1
Rejecting the null hypothesis indicates a statistically significant result.
What is the formula for CONFIDENCE.T() in Excel?
Confidence interval using t-distribution
This function calculates the confidence interval for the mean when using sample data.
What is the equation for Simple Linear Regression (SLR)?
ŷ = b0 + b1x
In SLR, b0 is the intercept and b1 is the slope of the regression line.
What does b0 represent in regression analysis?
Intercept (value of Y when X=0)
The intercept indicates the expected value of the dependent variable when all independent variables are zero.
What does b1 represent in regression analysis?
Slope (change in Y per unit X)
The slope indicates how much Y changes for a one-unit change in X.
What is the equation for Multiple Linear Regression?
ŷ = b0 + b1x1 + b2x2 + … + bkxk
Multiple linear regression involves multiple predictors to explain the dependent variable.
What does R² measure in regression analysis?
% of variance in Y explained by X
R² indicates the proportion of variation in the dependent variable that can be explained by the independent variables.
What is Adjusted R²?
Adjusts for number of predictors
Adjusted R² provides a better measure when comparing models with different numbers of predictors.
What are the assumptions of regression analysis?
- Linearity
- Independence
- Homoscedasticity (equal variance)
- Normality of residuals
These assumptions are crucial for the validity of regression results.
What does a p-value < 0.05 indicate?
Variable is significant
A p-value below the significance level suggests strong evidence against the null hypothesis.
What are the types of patterns in Time Series Forecasting?
- Horizontal (Stationary)
- Trend
- Seasonal
- Cyclical
- Random
Different patterns require different forecasting methods.
What is the Naïve forecasting method?
Forecast = last observed value
This method assumes that future values will be the same as the most recent observation.
What does MAE stand for in error metrics?
Mean Absolute Error
MAE measures the average magnitude of errors in a set of forecasts.
What does MSE stand for in error metrics?
Mean Squared Error
MSE measures the average of the squares of the errors, emphasizing larger errors.
What is MAPE?
Mean Absolute Percentage Error
MAPE expresses forecast accuracy as a percentage, useful for comparing across different scales.
What should you compare to choose the best forecast?
Compare MAE, MSE, MAPE across methods
Lower error metrics indicate a better model fit.
What Excel tool can be used for moving averages?
Data Analysis Toolpak or manual formulas
Excel provides built-in functions for calculating moving averages and visualizing forecasts.
