WorksheetsStatistics Final
Total questions: 54
Worksheet time: 47mins
What does the denominator of the correlation coefficient formula represent?
the combined slopes of X and Y
the averages of X and Y
the total variability of X and Y separately
the maximum value of X times the maximum value of Y
The third-variable problem can influence the interpretation of research results. Which of the following best describes this issue?
It occurs when an unmeasured variable influences both the independent and dependent variables, leading to a false association.
It refers to the inability to replicate research findings in different populations.
It is the result of using a small sample size in a study.
It happens when researchers intentionally manipulate data to achieve desired results.
The “Datasaurus” dataset and scatterplot that looks like a T-Rex teaches us that
strong correlations are always visible.
nonlinear patterns can exist even when r ≈ 0.
linear trends always dominate datasets.
visualizations are optional.
A major sign that an article is misrepresenting correlation research is:
It claims that correlation proves causation.
It discusses multiple variables.
It uses statistical graphs.
It mentions sample size.
Which of the following best explains why a small r value (e.g., r = .12) can still have a statistically significant p value?
The sample size is very large, making even small correlations statistically detectable.
The variables are related, as indicated by the r.
The data contains a major outlier that is pulling the correlation higher.
The standard deviations of the variables are both zero.
A study finds a positive correlation between the number of hours spent watching TV and weight gain. What is the most reasonable interpretation?
Watching TV causes weight gain directly.
Weight gain causes people to watch more TV.
TV programs influence metabolism.
There may be other lifestyle factors, like reduced physical activity, involved.
How does the regression line aid researchers in making predictions?
It matches each data point exactly to its predicted value.
It creates a visual summary of the average trend in the data and provides a formula for prediction.
It proves that one variable causes changes in the other variable.
It identifies outliers that do not fit the expected pattern.
A clinical psychologist is studying the relationship between the number of weekly therapy sessions (X) and clients’ depression scores (Y). She finds that as the number of therapy sessions increases, depression scores tend to go down. The regression line has a y-intercept of 25 and a slope of −2. Which of the following equations best represents the regression line?
Y = 25 − 2X
Y = 25 + 2X
Y = −2 − 25X
Y = −25 + 2X
Why is Ŷ (y-hat) referred to as the “least squared error” model in regression analysis?
It perfectly predicts each actual Y value, resulting in zero residuals.
It minimizes the sum of the squared differences between the observed Y values and the predicted Ŷ values.
It maximizes the strength of the correlation between X and Y.
It forces all data points to lie exactly on the line of best fit.
In a regression analysis, what does the value of R² tell you?
the strength of causation between the independent and dependent variables
the probability that the regression slope is statistically significant
the proportion of variance in the dependent variable that is predicted by the independent variable
According to the Venn diagram, what proportion of the variance in adult vocabulary size is explained by factors unique to adult vocabulary size?
20%
40%
60%
80%
Which statement best reflects the meaning of the R^2 (shared variance) in the Venn diagram?
Childhood reading fluency is the only important predictor of adult vocabulary size.
Childhood reading fluency explains some, but not most, of the variability in adult vocabulary size.
Childhood reading fluency and adult vocabulary size are completely independent.
Childhood reading fluency explains nearly all the variability in adult vocabulary size.
Looking at the regression line, is it reasonable to assume that infinitely older phones will continue to cost less and less, possibly to the point of becoming free or negative in price?
Yes. That is exactly what we should conclude based on the regression line.
No. Although the price will continue to decrease, we cannot conclude that age perfectly determines smartphone prices.
No. Regression does not imply causation, and there are limits to what a regression equation can reasonably predict.
No. Although there is a negative relationship between phone age and price, we cannot assume prices will decrease forever.
An industrial/organizational (I/O) psychologist is studying the relationship between the number of professional development hours employees complete and their annual performance review scores. According to the scatterplot provided, what type of relationship exists between professional development hours and performance review scores?
Positive linear relationship
Negative linear relationship
No relationship
Curvilinear relationship
An industrial/organizational (I/O) psychologist is studying the relationship between the number of professional development hours employees complete and their annual performance review scores. X (predictor): Number of professional development hours completed. Y (outcome): Performance review score (0–100). What is the value of R (correlation coefficient) reported in the model summary?
0.912
0.512
0.091
0.301
The R Square value of 0.832 indicates that:
83.2% of the variance in the dependent variable is explained by the model.
The model is perfect and explains 100% of the variance.
The model explains only 8.32% of the variance in the dependent variable.
The model is not useful for prediction.
An industrial/organizational (I/O) psychologist is studying the relationship between the number of professional development hours employees complete and their annual performance review scores.
• X (predictor): Number of professional development hours completed
• Y (outcome): Performance review score (0–100)What is the best interpretation of the unstandardized coefficient (B = 0.79) for professional development hours?
Employees with higher development hours have lower performance scores.
Each additional hour of professional development predicts about a 0.79-point increase in performance review score.
Each additional hour of professional development predicts about a 79-point increase in performance review score.
Professional development hours are not significantly related to performance scores.
An industrial/organizational (I/O) psychologist is studying the relationship between the number of professional development hours employees complete and their annual performance review scores. What does the R² value of .832 mean in this regression analysis?
83.2% of the variance in performance review scores can be explained by professional development hours.
83.2% of the variance in professional development hours can be explained by performance scores.
There is an 83.2% chance of making a prediction error.
83.2% of employees had perfect prediction scores.
Suppose you ran a regression analysis predicting performance review score from professional development hours. The SPSS output shows the following coefficients: Coefficients Predictor B Beta t Sig. (Constant) 50.26 — 4.55 .001 Professional Development Hours (X) 0.79 .912 12.22 .000 Note: The data included in this question were generated by the author for instructional purposes only. Which value is the Y intercept and which value is the slope (b)?
0.79; 50.26
50.26; .912
50.26; 0.79
.912; 50.26
Suppose you ran a regression analysis predicting performance review score from professional development hours. The statistical output yields the following coefficients (see image). Based on the output, which of the following is the correct regression equation for predicting performance review score from professional development hours?
Ŷ = 50.26 + 0.79(X)
Ŷ = 0.79 + 50.26(X)
Ŷ = 50.26 – 0.79(X)
Ŷ = 0.79(X)
A social psychologist studied the classic bystander effect by examining how the number of people present during a staged emergency affects how long it takes someone to intervene. A portion of the output is shared in the image. Which of the following best identifies and interprets the standardized beta for group size?
The beta is 2.24, meaning that each additional person increases intervention time by about 2.24 seconds.
The beta is .93, meaning that group size has a strong positive relationship with intervention time.
The beta is .93, meaning that group size explains 93% of the variation in intervention time.
The beta is 12.19, meaning that intervention time increases by 12.19 seconds per person.
Suppose you ran a regression analysis predicting performance review score from professional development hours. The statistical output yields the following coefficients. See image. An employee completed 20 professional development hours. Using the regression equation, what is their predicted performance score?
65.8
66.1
50.3
80.1
A researcher reports the following regression results: β = .13 R² = .02 p = .003 Which of the following is the most accurate evaluation of these results?
Although the predictor is statistically significant, it explains very little variance and may not be practically meaningful.
The predictor explains a substantial portion of the variance and is statistically significant.
The predictor is practically strong but statistically nonsignificant.
R² = .02 indicates a 2% error rate, so the model is inaccurate.
A regression model shows that an artist’s number of social media followers predicts their concert ticket sales. Why might predictions based on this regression model become less accurate over time?
Regression proves that more followers will always cause higher ticket sales, even as trends change.
Regression describes the relationship within the data collected at one point in time, but future changes in social media use could weaken the relationship.
Regression predicts future ticket prices based on changes in social media platforms.
Regression can automatically adjust for changes in fan behavior over time without new data.
In a regression analysis, a researcher finds a statistically significant p value and an R² value of .04. What is the best interpretation of these results?
The regression is both statistically significant and practically strong.
The regression is statistically significant but not practically strong; the independent variable explains very little of the variance in the dependent variable.
The regression is not statistically significant; however, the independent variable explains almost all of the variance in the dependent variable.
The independent variable strongly predicts changes in the dependent variable.
The third-variable problem refers to a situation where a third factor influences both variables being studied, making it difficult to determine if there is a direct relationship between them. Which of the following is an example of the third-variable problem?
A researcher finds a correlation between ice cream sales and drowning incidents, but both are actually influenced by temperature.
A study shows that eating carrots improves eyesight, but no third variable is involved.
A survey finds that people who exercise more have higher incomes, with no other factors considered.
A scientist observes that students who study more get better grades, without considering other influences.
Self-Esteem Crisis: Students take a spelling test with known population mean and SD. You want to see how extreme each student is compared to the population. What analysis do you calculate?
Opinion based question: What’s one thing from this class that will stick with you in the real world?
(You know… the thing that will pop back into your brain randomly when you’re living your best life, even long after the semester stops pretending it's Week 67.)
Opinion based question: What was your favorite part of this class — the thing that made your brain sparkle just a little?
Opinion Based Question: And what was just… not giving?
(Be so for real. What didn’t land, didn’t vibe, or didn’t spark joy?)
