CNSL503 / CNSL 503 Module 7 Statistics 2026/2027 | Portage Learning | Verified Questions & Answers | 100% Correct | Grade A

CNSL503 / CNSL 503 Module 7 Statistics 2026/2027 | Portage Learning | Verified Questions & Answers | 100% Correct | Grade A Q: ___ is performed to measure and describe how two quantitative variables are related Answer Correlational analysis Q: Correlational analysis is performed when variables are observed in their ___ rather than being manipulated in a study Answer observed in their natural state Q: ___ describes the direction of a relationship, form of a relationship (linear, curvilinear, quadratic, or cubic), and the degree of a relationship. Answer Correlation Q: ___ describes the direction of the linear relationship between two variables Answer Covariance Q: If two variables covary, one of two directions exist in the plot of variables: 1. 2. Answer 1. Both variables increase or decrease together. OR 2. As one variable increases the other decreases Q: Covariance does not imply __ Answer Covariance does not imply causation Q: ___ is a limitation of correlational studies, however, correlation being established is the first step in determining ___ Answer Causation, causality Q: The most common ways correlations are represented graphically are with ___, a graph in which two measurements are obtained from each individual in the study and paired variable scores are plotted as coordinate pairs. Answer scatterplots Q: In scatterplots, the independent variable is on the ___ and the dependent variable is on the __ Answer In scatterplots, the independent variable is on the x-axis and the dependent variable is on the y axis. Q: In scatterplots, the independent variable is called the ___ and the dependent variable is called the __ Answer explanatory, response Q: A linear relationship describes when plotted pairs ___ Answer approximate a straight line Q: A positive correlation indicates Answer that both variables are increasing together Q: A negative correlation indicates Answer that an increase in the explanatory variable results in a decrease in response variables Q: No correlation indicates Answer There is no relationship between two variables, on a scatterplot points are spread out and do not resemble a straight line. Q: When values of two variables appear to be related, but the relationship does not follow a linear pattern, this is called a ___ relationship Answer nonlinear or curvilinear relationship (for example exponential relationship) Q: The ___, Pearson's r, measures the degree of linear relationship or consistency of the relationship Answer correlation coefficient r = -1 indicates Answer perfect negative relationship, perfectly inverse relationship between x and y Q: r=0 indicates Answer no correlation Q: r = +1 indicates Answer perfectly positive relationship between x and y Q: Researchers typically look for a correlation coefficient of what values before considering a relationship between two variables? Answer r-0.05 or r0.05 Q: r =0.7 to 0.9 indicates a Answer high correlation Q: r= 0.5 to 0.7 indicates Answer moderate correlation Q: r=0.3 to 0.5 indicates Answer low positive correlation Q: r=0.0 to 0.3 indicates Answer very weak or negligible correlation Q: As the r-values move closer to +1 and -1, the points resemble ___ Answer straight lines ___ results in smaller correlation coefficients and inaccurate relationship measures between two variables Answer Range restriction True/False: Correlational analysis is not impacted by outliers Answer False, correlational analysis is impacted by outliers ___ is a correlation coefficient that is calculated to determine the degree and direction of the relationship between X and Y if a linear relationship exists. Answer Pearson's r Pearson's r is a sample statistic, whereas __ is the population parameter ρ "rho" Pearson's r is defined by what ratio? r = degree to which X and Y vary together (covariability) / degree to which X and Y vary separately (separate variability) ___ involves making specific assumptions about populations and are used when a population has a normal distribution, samples have equal variances, a linear relationship, and independent variables. Examples: ANOVA, t-tests, z-tests, Pearson's r Parametric tests __ involves making no assumptions about the population parameters when data are not normal and a correlation needs to be determined Nonparametric test aka distribution-free tests ____ is a nonparametric test used to determine correlations, used for ordinal data or for non normal continuous data, ie data converted to ranks, sometimes used with normal data as it is not sensitive to outliers Spearman's ρ Outliers in correlation coefficients can cause inaccurate conclusions to be drawn from researchers due to skewed results True/false Outliers can be a result of true values True State possible hypotheses for Pearson's r Ho: ρ = 0 (No relationship between variables) Ha: ρ ≠ 0 (Non-directional relationship) OR Ha: ρ0 (Predirected positive relationship) OR Ha: ρ0 (Predirected negative relationship) How to establish decision criteria with Pearson's r df = N - 2 (N = # of ordered pairs) Use alpha, df, and number of tails with an rcrit table to determine rcrit value APA format for Pearson's r There is a very strong negative correlation between X and Y, r(3) = -0.959, p=0.01 ___ is the process of calculating the equation of the line that best represents or "fits" the data Linear regression True/false Linear regression is completed after a correlation is determined to draw inferences about predictions. True A ___ serves as the center of data to make predictions about values not actually in the dataset, similar to central tendency in a distribution. It is the best way to describe the dataset as a whole, like a mean best-fit or regression line The best fit regression line always passes through what pair of coordiantes? (x̄,ȳ ) The mean for x, The mean for y True/false Linear regression creates a prediction, it does not guarantee exact values True What is the regression equation? y=bx+a b=slope a=y-intercept (x, y) = pair of coordinates In model coefficient statistical software output tables, where do you identify the slope and y intercept? Where do you ID the statistical significance? Under estimate, the first value is y-intecept, the second value is the slope. y=slopex+y-intercept Statistical significance is the bottom row P value In a Model Fit Measures model test, how do you identify the regression equation and statistical significance? Calculated F ratio listed under F. determine if this exceeds the Fcrit use df1, df2. F(df1, df2) = Fcalc, p-value How do you report a regression equation in APA format? The equation Y=slopex+y-intercept is/is not statistically significant in predicting Y from X. F(df1, df2) = Fcalc, p-value Example: The equation Y=32x+1 is statistically significant in predicting cost of a diamond from weight in carats. F(1,21)=32, p0.001 __ is the amount of variation of y values that can be explained by changes in the x values. (the degree to which the variance of a variable is expressed by the best fit line_ Proportion of variance accounted for The coefficient of determination is represented by r² The r² ratio compares variance explained by the model/total variance, an effect size A larger r² indicates smaller error, more precise predictions A smaller r² indicates larger error, less precise predictions an r² value of 0.17 indicates 17% of variability in Y can be predicted from X Why is it important to interpret r² in context? A value of 0.5 may indicate a strong correlation in a field like human behavior, but in a field like manufacturing, a value of 0.5 may not indicate a strong enough correlation for a quality product to be created An r-value of 0.77 and r² value of 0.604 value indicates R value of 0.777 indicates a moderate to strong positive correlation, and r² value indicates 60.4% of the variability in the Y can be predicted from X, this is a large effect size. ____ involves finding the best-fit equation for three or more variables, namely, one response variable (dependent variable), and two or more explanatory variables (independent variables). Multiple regression While ______ is the parametric correlation test, _______ is the non-parametric correlation test. Pearson's; Spearman's What are limitations of correlational analyses? Sensitive to outlier, cannot be used to determine causation, and require an unrestricted range If R=-.451, R^2=0.203, F=3.31, df1=1 ,df2=13, p =0.092 Interpret the results of this correlational analysis Answer: There is a low positive correlation between X and Y,