Correlation Coefficients Quiz

<p>The sum of the residuals is always zero</p> Signup and view all the answers

<p>$Y = 2.034 + 0.374X$</p> Signup and view all the answers

<p>$s^2 = SSE/(n-2)$</p> Signup and view all the answers

<p>The model assumes that the random error term has a mean of zero.</p> Signup and view all the answers

<p>$E(Y) = \beta_0 + \beta_1X$</p> Signup and view all the answers

<p>Least squares method</p> Signup and view all the answers

<p>The least squares estimators are unbiased estimators.</p> Signup and view all the answers

<p>As one variable increases, the other variable decreases</p> Signup and view all the answers

<p>The variables are uncorrelated</p> Signup and view all the answers

<p>The population correlation coefficient</p> Signup and view all the answers

<p>To test whether there is a linear relationship between two variables</p> Signup and view all the answers

<p>Assumption of homogeneity of variance</p> Signup and view all the answers

<p>The proportion of the variability in the dependent variable explained by the independent variable</p> Signup and view all the answers

<p>Time series data</p> Signup and view all the answers

<p>$R^2 = 1 - SSE/SS(Total)$</p> Signup and view all the answers

<p>P-P plot</p> Signup and view all the answers

<p>To test the significance of the whole set of independent variables</p> Signup and view all the answers

<p>t = b0 / s(b0)</p> Signup and view all the answers

<p>It is normal for the normal error model</p> Signup and view all the answers

<p>var(i) = σ^2[(1/n) + (Xi - X)^2/SSxx]</p> Signup and view all the answers

<p>They are sensitive to departures from normality of the error terms distribution</p> Signup and view all the answers

<p>The main purposes of regression analysis are descriptive and predictive. Descriptive regression analysis examines the kind of relationship between variables and its strength, while predictive regression analysis uses the equation relating the dependent variable (Y) and the independent variable (X) to predict the value of Y for a given value of X.</p> Signup and view all the answers

<p>The two different situations in regression analysis are: (a) Y is a random variable and X is a fixed, non-random variable. (b) Both Y and X are random variables.</p> Signup and view all the answers

<p>The matrix approach to linear regression analysis involves representing the regression model using matrix notation. The regression equation can be written as: $Y = X\beta + \epsilon$, where Y is the vector of dependent variable values, X is the matrix of independent variable values, $\beta$ is the vector of unknown coefficients, and $\epsilon$ is the vector of random error terms.</p> Signup and view all the answers

<p>The assumption of homogeneity of variance in a regression model states that the spread of the residuals should not increase or decrease with the values of the independent variable or with the predicted values.</p> Signup and view all the answers

<p>The critical assumption of the simple linear regression model is that the error terms associated with each xi have a normal distribution.</p> Signup and view all the answers

<p>One way to compare the observed distribution of residuals to that expected under the assumption of normality is to plot the two cumulative distributions against each other for a series of points. If the two distributions are identical, a straight line results. This plot is called a P-P plot (a cumulative probability plot).</p> Signup and view all the answers

<p>$s(b1) = \sqrt{\frac{s^2},{SS_{xx}}}$</p> Signup and view all the answers

<p>$b0 - t_{\alpha/2}s(b0) &lt; \beta_0 &lt; b0 + t_{\alpha/2}s(b0)$</p> Signup and view all the answers

<p>$\hat{Y} = b0 + b1X$</p> Signup and view all the answers

<p>$s^2 = \frac{SSE},{n-2} = \frac{SS_{yy}-b1SS_{xy}},{n-2}$</p> Signup and view all the answers

<p>$r = \frac{SS_{xy}}{\sqrt{(SS_{xx})(SS_{yy})}}$</p> Signup and view all the answers

<p>The purpose of the t-test for correlation is to test whether there is a linear relationship between two variables by testing whether the population correlation coefficient, ρ, is equal to zero.</p> Signup and view all the answers

<p>If the absolute value of the calculated t-value is greater than the critical t-value, we reject the null hypothesis and conclude that there is a significant linear relationship between the variables.</p> Signup and view all the answers

<p>The standardized regression coefficient, also known as beta, is equal to the correlation coefficient, r.</p> Signup and view all the answers

<p>The null hypothesis being tested is H0: β0 = 0.</p> Signup and view all the answers

<p>The t-value in the hypothesis test of β0 is calculated using the formula t = b0 / s(b0).</p> Signup and view all the answers

<p>The (1 - α) 100% confidence interval for the mean response E(Yi) is given by i - tα/2, (n-2) s(i) &lt; E(Yi) &lt; i + tα/2, (n-2) s(i).</p> Signup and view all the answers

<p>The (1 - α) 100% prediction interval for a new response Yi(new) is given by i - tα/2, (n-2) s(predi) &lt; Yi(new) &lt; i + tα/2, (n-2) s(predi).</p> Signup and view all the answers

<p>R2=SSR/SS(Total) = 1 - SSE/SS(Total) = b1SSxy/SSyy and 0 ≤ R2 ≤ 1.</p> Signup and view all the answers

<p>The ANOVA table provides an overall test of the significance of the whole set of independent variables.</p> Signup and view all the answers

<p>The correlation coefficient ρ = σXY/σXσY is a measure of the direction and the strength of linear association between two variables.</p> Signup and view all the answers

<p>The F-statistic is F = (n-2)R2/(1-R2).</p> Signup and view all the answers

<p>The general form of a probabilistic model is $Y = $ Deterministic component + random error.</p> Signup and view all the answers

<p>The formula for the simple regression model is $Y = f(X) + \epsilon$.</p> Signup and view all the answers

<p>The formula for the multiple regression model is $Y = f(X_1, X_2, ..., X_k) + \epsilon$, where $k \geq 2$.</p> Signup and view all the answers

<p>The simple linear regression model is $f(X) = \beta_0 + \beta_1X$.</p> Signup and view all the answers