What statistical method models relationships between dependent and independent variables?

Regression analysis

The regression equation y = a + bx has slope b = 0.75. What does this mean?
A) y decreases 0.75 units per x unit
B) y increases 0.75 units per x unit
C) y equals 0.75 when x = 0
D) No relationship exists

B) y increases 0.75 units per x unit

True or False: The correlation coefficient r can have values greater than 1.0.

False. The correlation coefficient r always ranges from -1 to +1.

In the formula b = (nΣxy - ΣxΣy)/(nΣx² - (Σx)²), what does b represent?

The slope of the regression line

A correlation coefficient of r = -0.85 indicates what type of relationship?

Strong negative linear relationship

What does r² = 0.64 mean in regression analysis?
A) 64% of y variation is explained by x
B) Correlation is 0.64
C) 36% error rate
D) Perfect correlation

A) 64% of y variation is explained by x

The least squares method minimizes the sum of _____ between observed and predicted values.

Squared deviations

If residual = observed - predicted = -5, what does this indicate?

The model overestimated the actual value by 5 units

Why are prediction intervals wider than confidence intervals for the same data?

They account for both estimation uncertainty and individual observation scatter

What is the degrees of freedom for simple linear regression with 15 data points?

13 (calculated as n - 2 = 15 - 2)

True or False: A regression line always passes through the point (x̄, ȳ).

True. The regression line always passes through the means of x and y.

Which correlation shows stronger linear relationship?
A) r = +0.6
B) r = -0.8
C) r = +0.4
D) r = -0.3

B) r = -0.8

Standard error of estimate (sₑ) measures the _____ of observed values around the regression line.

Variability

Given regression y = 10 + 2x, what is the predicted y when x = 5?

20

What assumption requires residuals to have constant variance across all x values?

Homoscedasticity

In multiple regression y = β₀ + β₁x₁ + β₂x₂, what does β₀ represent?
A) Slope for x₁
B) Slope for x₂
C) y-intercept
D) Error term

C) y-intercept

When is adjusted r² preferred over regular r² in regression analysis?

In multiple regression to account for number of predictors

A residual of |e| > 2sₑ typically indicates what about that data point?

It may be an outlier requiring investigation

True or False: Strong correlation always implies causation between variables.

False. Correlation does not imply causation; other factors may be involved.

To linearize y = ax^b, which transformation should be applied to both variables?

Take natural logarithm of both x and y

If Σ(residuals) ≠ 0 in your regression analysis, what does this suggest?

There may be an error in calculations or model assumptions