CWP test with 100% correct answers 2024

I am using x to predict y. When I know the value of x, the mean-squared-error of my estimate of y is less than when I don't know x. - answer-x explains some of the variance in y If the SSmodel is greater than the SSresidual... - answer-the model accounts for more than 50% of the total variance What is the coefficient of determination? - answer-The proportion of variance accounted for in the dependent variable by the predictor variables. What is the relationship between r and beta in a simple regression? - answer-beta is an unstandardised measure of r What is the critical value for t with 5 degrees of freedom and an alpha of 0.05 two-tailed? Give your answer to 2 decimal places. - answer-2.57 You have the following data: x = c(10,3,2,1,3,4,5,6) y = c(2,14,18,12,10,11,8,9) You run a linear model and get the following estimate of the slope: ^B1 = -1.423 What is the standardised beta? Report to 2 decimal place - answer--0.86 If I have a lot of error in my regression model, it means that: - answer-There are big differences between the line specified by my model and the corresponding points on the scatterplot. If the beta for your x term in a regression model is negative, it means: - answer-That there as x increases, y decreases. I conduct a study to investigate whether average hours of sleep per nigh (x) predicts sick days per year (y). I find the follow values for the intercept and slope: B0 = 25 B1 = -1.6 True or false, the following is the correct interpretation of the intercept: A person who sleeps 0 hours on average per night is expected to have 24 sick days per year. - answer-False I conduct a study to investigate whether average hours of sleep per nigh (x) predicts sick days per year (y). I find the follow values for the intercept and slope: B0 = 25 B1 = -1.6 True or false, the following is the correct interpretation of the slope: For every hour of sleep a person has on average per night, the number of sick days per year decreases by 1.6 days. - answer-True What is the critical value for t with 5 degrees of freedom and an alpha of 0.01 two-tailed? Give your answer to 2 decimal places in the form X.XX - answer-4.03 You run a linear model with a single binary predictor. The intercept for the model is 110, and the unstandardized beta is 17.1. What is the mean of the group coded 1? - answer-127.1 You run a linear model with a single binary predictor (0 = Group0; 1 = Group1). The mean of Group1 is 75 and the beta coefficient is 7. What is the value of the intercept? - answer-68 If regression model errors (residuals), show different amounts of variation across the range of measurement, they are referred to as ... - answer-Heteroscedastic Match the assumption/diagnostic to the most appropriate test. Shapiro-Wilk Test - answer-Normality of residuals Match the assumption/diagnostic to the most appropriate test. Durbin-Watson Test - answer-Autocorrelation of residuals Match the assumption/diagnostic to the most appropriate test. Non-constant variance test - answer-Heteroscedasticity Match the assumption/diagnostic to the most appropriate visualization. Histogram - answer-Normality of residuals Match the assumption/diagnostic to the most appropriate visualization. Scatterplot - answer-Linearity Match the assumption/diagnostic to the most appropriate visualization. Residual-vs-predicted plot - answer-Heteroscedasticity The null hypothesis for the non-constant variance test (Breusch-Pagan test) is that the data are heteroscedastic. True or False? - answer-False What are the degrees of freedom for the sums of squares total in a linear model? - answer-n-1 Which R function can be used to calculate from a model object? - answer-predict() In a simple linear model where both variables are continuous and z-scored, what is the value of the intercept? - answer-0 The null hypothesis for the non-constant variance test (Breusch-Pagan test) is that the data are heteroscedastic. True or false? - answer-False In testing model assumptions and appropriateness, what quantities summarise the influence of an individual case on the predicted values for that same case? - answer-Cook's distance Given the following: hat y = 10.5 + 4.3*x What is the predicted score for someone scoring 7 for x? Give you answer to two decimal places in the form X.XX - answer-40.60 Assuming we have a data set called df, that contains variables called DV and IV, the following R code will run without error? lm(DV ~ IV data = df) True or false? - answer-False In multiple regression high leverage values would have... - answer-X values far from the centroid of X Suppose we have a study with: Sample size (n) = 73 Number of predictors (k) = 11 Which of the following would be considered high influence cases based on Di 4/(n-k-1) ? - answer-Cook's distance = 0.09 What is the critical value for F with 5,58 degrees of freedom and an alpha of 0.05? Give your answer to 2 decimal places in the form X.XX - answer-2.37 Given the following linear model equation: y = 10 + 6x(1) + 2x(2) + 3x(3) What would the predicted score for Y be for an individual with the following scores: x1 = 2 x2 = 6 x3 = 0 - answer-34 I have a categorical variable (`condition`) with 4 levels and the following group means: Control = 32 Group 1 = 23 Group 2 = 10 Group 3 = 5 I use this variable to predict an outcome variable (`test_score`). The two variables are in a data frame called `df`. I run the following code in R: contrasts(df$condition) - ment(4, based = 2) lm(test_score ~ condition, data = df) What will b3 equal in this model? Report your answer in the form X.XX - answer--18 (The code uses dummy codes, but sets Group 1 as the reference group. b3 will code for the third comparison, which will be the difference between Group 3 and Group 1. (Group 3 - Group 1 = 5 - 23 = -18.00)) I have the following linear model equation: y = 10 + 6x(1) + 2x(2) + 3x(3) What does the beta of x1 mean? - answer-That a one unit change in x1 produces a six unit change in y when all other variables are held constant. All else being equal, which of these will increase the predictive power of your linear model? - answer-Increasing the variance in (one of) your predictor(s) I have a categorical predictor with 7 levels. How many dummy coded variables are required in a linear model to fully represent the variable? - answer-6 Highly correlated predictors make the standard error of the coefficients smaller. True or false? - answer-False, correlated predictors make us less certain about the effect of a single variable, and thus make the SE larger. I run the following linear model: DV = b0 + b1x1 + b2x2 + b3x3 +b4x4 + e In a sample of 200 participants. I have an r-squared value of 0.27. What is my adjusted r-square? Report to 2 decimal places in the form X.XX - answer-0.26 (Formula: 1 - (1-Rsquared) x [(N-1)/N-k-1] What are the two features of a model which form part of the adjusted r-square calculation? - answer-Sample size and number of predictors The mean square model is calculated by: - answer-Dividing the sum of squares for the model by k, where k is the number of predictors. Mean squares calculations divide sums of squares by the associated degrees of freedom. Degrees of freedom connected to models will be focused on the number of predictors. A researcher collects some data on three variables, overall degree performance (DV, out of 100), conscientiousness (x1, mean centred) and neuroticism (x2, mean centred). The researcher fits the following model: lm(performance ~ conscientiousness + neuroticism + conscientiousness*neuroticism) And gets the following parameter estimates: b0 = 46.5 b1 = 9.2 b2 = 6.2 b3 = 10.0 Calculate the crossing point for conscientiousness. Report your answer to 2 decimal places. - answer--0.62 For the conscientiousness crossing point, we need to divide, -b2/b3, or -6.2/10 In a region of significance analysis, two values are produced. What do these two values represent? - answer-The thresholds of Z at which the simple slopes of Y on X become significant In the following model, what type of effects are b1 and b2? Y= b0 + b1x + b2z +b3xz + e - answer-Conditional (marginal) effects It is conditional in that the interpretation is "conditioned on", or evaluated at, a specific value of the moderator. A researcher fits the following model on uncentered X and Z variables: Y= b0 + b1x + b2z +b3xz + e The researcher then centers X and Z, and re-estimates the model. Which of the model beta coefficients will not change? - answer-b3 (The highest order term in a model is invariant to lower order scaling. So here, beta3 for the interaction will not change. Both variables were rescaled, meaning both lower order terms (b1 and b2) will change.) An interaction where the effect of one variable on an outcome is weakened by a second variable is known as... - answer-a buffering interaction In a disordinal interaction, the crossing point falls outside the plausible range of the variable. True or false? - answer-False A researcher collects some data on three variables, overall degree performance (DV, out of 100), conscientiousness (x1, mean centred) and department a student comes from (0=Chemistry, 1 = Physics). The researcher fits the following model: lm(performance ~ conscientiousness + department + conscientiousness*department) And get the following parameter estimates: b0 = 52.5 b1 = 5.4 b2 = 10.2 b3 = 8.5 What is the mean score for Physics students with average levels of conscientiousness? Report your answer to 1 decimal place. - answer-62.7 The question asks for the intercept at the average value for a mean centred variable, or, at 0. Recall this is the interpretation of our conditional main effects. So here, we need to add the coefficient for the binary variable to the intercept from the model. How do you work out the simple slope for the following interaction model, where all variables are z-scores. Y = beta0 +beta1x + beta2z + beta3xz - answer-beta1 + beta3, given that the variables are z-scores I have a data set called `df` containing 3 variables; Y, X1 and X2. I run the following linear model res - lm(Y ~ X1 + X2, data = df) True or false, the following R-code would produce a histogram of model residuals. tb - tibble(res = tib$srh - m1$s) tb %% ggplot(tb, aes(x=res)) + geom_histogram() - answer-True A case has a high COVRATIO value, but a low dfbeta. What is the most likely reason? - answer-It has an extreme value on X but is not a regression outlier If regression model errors (residuals), show the same amount of variation across the range of measurement, they are referred to as ... - answer-Homoscedastic What values are plotted on the the Y-axis of a component-residual plot as plotted by the crPlots() function? - answer-Partial residuals Which of the statements below which are necessarily true: - Outlying residuals will influence your model estimates - Residuals with high leverage will influence your model estimates - Outlying residuals with high leverage will influence your model - Some of your residuals will be outliers - answer-- Outlying residuals with high leverage will influence your model What does the variance inflation factor measure? - answer-How much se(beta) is increased by predictor correlations In an all-possible-regressions model with 11 predictors, how many possible models will there be? - answer-2048 The F-test for model utility in a linear model with multiple predictors is the same as the square t-statistic for the significance of a model coefficient? - answer-False. The F-test is a test of all slopes (or the whole model). With a single predictor the answer here would be true. How can you get the coefficients from a model? - answer-summary(model)$coefficients A researcher wishes to compare a set of non-nested regression models (n=200) using the strongest penalty for model complexity. Which of the following should the researcher select? - answer-BIC The following two models are nested: Y = b0 + b1x1 + b2x2 + b3x3 + e Y = b0 + b3x3 + b4x4 + e True or false? - answer-False. Not all the betas from the first model are included in the second, as well as the beta4 At the bottom of the summary(model) output you will find the f statistic. True or false, this is equivalent to a model comparison between the model tested and the intercept only model? - answer-True I run a model to predict a health composite variable from three IVs, on a sample of 200 participants. I then fit another model where I add a 4th IV. The 4th IV has missing data and my sample size drops to 197. I compare these two models using a non-nested model comparison. True or False, my test is valid? - answer-False Which of the following tools can be used to compare nested models on the same data? - answer-AIC, BIC, Incremental F I run the following code: res - lm(y ~ x1 + x2 + x3, data = df) plot(res, which = 2) What plot is produced? - answer-Normal QQ plot A colleague comes to seek your opinion. They provide you with the F-test for two models. They share the following: Model 1: F(2,81) = 30.1, p .001 Model 2: F(3,81) = 28.4, p.001 They also share that both models are using a subset of variables from a much larger data set. The outcome variable is the same in both models. Model 1 and 2 share 1 predictor, the other predictors vary. The total sample size for the whole data set is 150. You are asked if you think these models can be formally compared. Which of the following answers would you give? - answer-No, not based on the info provided - the degrees of freedom for the F-test suggest that the same number of participants are in both models, but as their are unique predictors in both models, it is possible these are not the same participants. We could not decide this without seeing the pattern of missing data. (see lecture slides for discussion) You run a linear model with a single binary predictor (0 = Group0; 1 = Group1). The mean of Group1 is 50 and the beta coefficient is 16. What is the value of the intercept? - answer-34 b1 = G1 - G0 16= 50 - G0 G0 = 34 I have a categorical predictor with 8 levels. How many dummy coded variables are required in a linear model to fully represent the variable? - answer-7 An interaction where the effect of one variable on an outcome is strengthened by a second variable is known as... - answer-a synergistic interaction A colleague comes to seek your opinion. They provide you with the F-test for two models. They share the following: Model 1: F(2,101) = 45.1, p .001 Model 2: F(3,97) = 26.4, p.001 They also share that both models are using a subset of variables from a much larger data set. The outcome variable is the same in both models. Model 1 and 2 share 1 predictor, the other predictors vary. The total sample size for the whole data set is 150. You are asked if you think these models can be formally compared. Which of the following answers would you give? - answer-No, because the sample sizes differ. You can see from the degrees of freedom for the F test that the N is different as the value for the residual df (the second value) is different. When you have a significant interaction term in a linear regression model, it means that... - answer-The slope of one predictor variable changes at different levels of the other predictor variable. Given the following linear model equation: y = 9 + 3x1 + 2x2 + 5x3 What would the predicted score for Y be for an individual with the following scores: x1 = 1 x2 = 2 x3 = 7 - answer-51 Which of the following tools can only be used to compare models that are nested? - answer-Incremental F I have a categorical variable (`condition`) with 4 levels and the following group means: Control = 30 Group 1 = 20 Group 2 = 10 Group 3 = 5 I use this variable to predict an outcome variable (`test_score`). The two variables are in a data frame called `df`. I run the following code in R: contrasts(df$condition) - ment(4, based = 3) lm(test_score ~ condition, data = df) What will b2 equal in this model? Report your answer in the form XX.XX (including signs if necessary) - answer-10.00 (The code uses dummy codes, but sets Group 2 as the reference group. b2 will code for the second comparison, which will be the difference between Group 1 and Group 2. (Group 1 - Group 2 = 20-10 = 10.00)) The F-test for the main effect of a experimental condition in a one-way ANOVA is the same as the model F-test for the linear model containing dummy or effect coded variables representing the experimental condition. True or false? - answer-True I run the following models: m1 - lm(DV ˜ Group, data = df) m2 - lm (DV ˜ Group + cov, data = df) anova(m1, m2) The resultant test from anova() gave me a p-value of 0.63. What does this mean? - answer-The inclusion of cov did not significantly reduce the residuals sums of squares. I have a 3 way within persons design. How many IVs do I have? - answer-3, an n-way experiment design has n IVs I have a 3 way within persons design. How many experimental groups does each participant exist within? - answer-More than 1. In an experimental design, the within group variation contains both variation due to the experimental condition, and error variation. True or false? - answer-False I have an experiment where I am looking at the effect of study time on word recall. I have a between persons design with 4 groups (10 minutes of study, 20 mintues of study, 30 minutes of study, and 40 minutes of study). After studying a list words for some amount of time, participants recall as many words as possible. I analyse my data and find a I have a significant F value. What does this result mean? - answer-There is some difference between the amount of study time and the number of words recalled. The F test is an omnibus test, giving me information on whether there was some effect of my experimental variable. You have the following data for a 2x2 experiment where the effect of emotional state (calm, anxious), and study type (massed vs. spaced) on exam performance was examined. The following data was collected: Calm-massed: Mean = 4.5 Calm-spaced: Mean = 6.7 Anxious-massed: Mean = 5.9 Anxious-spaced: Mean = 7.9 The data is analysed with a regression model using effects coding, where x1 codes emotional state (1 = calm, -1 = anxious), and x2 codes for study type (1 = massed, -1 = spaced). You run your model as: performance ~ emotion + studytype + emotion*studytype What is the b3 term? Answer to 2 decimal place in the form X.XX - answer--0.05 A researcher conducts an experiment with a 3x3 factorial design. The researcher analyses the data using dummy coded variables. Factor 1 (F1), has 3 levels (A, B, C) where level A is the reference group. This is coded with 2 dummy variables D1 and D2. Factor 2 (F2) has 3 levels (A, B, C) where level A is the reference group. This is coded with 2 dummy variables D3 and D4. Which is the correctly written linear model including variables for all interactions? - answer-y = b0 + b1D1+ b2D2+ b3D3+ b4D4+ b5D1D3+ b6D1D4+ b7D2D3 + b8D2D4 The best way to approach a question like this is to first work out how many terms there should be (r-1) + (c-1) + (r-1)(c-1), so here 2 + 2 + 4 = 8 terms. From there you want to check that the subscripting is correct, particular for the interactions which need to cross levels from F1 with levels from F2. Within factor crossing is going to be an incorrect specification. A researcher conducts an experiment with a 4x3 factorial design, and analyses it with a regression model using dummy codes (Variable labels: 4-level factor = x1, x2, x3; 3-level factor = x4, x5). They find a significant interaction for the x2:x5 term, but no other interaction terms are significant. This means: - answer-There is a significant interaction You have the following data for a 2x2 experiment where the effect of emotional state (calm, anxious), and study type (massed vs. spaced) on exam performance was examined. The following data was collected: Calm-massed: Mean = 4.5 Calm-spaced: Mean = 6.7 Anxious-massed: Mean = 5.9 Anxious-spaced: Mean = 7.9 The data is analysed with a regression model using effects coding, where x1 codes emotional state (1 = calm, -1 = anxious), and x2 codes for study type (1 = massed, -1 = spaced). You run your model as: performance ~ emotion + studytype + emotion*studytype What is the b1 term? Answer to 2 decimal place in the form X.XX - answer--0.65 You have the following data for a 2x2 experiment where the effect of emotional state (calm, anxious), and study type (massed vs. spaced) on exam performance was examined. The following data was collected: Calm-massed: Mean = 4.5 Calm-spaced: Mean = 6.7 Anxious-massed: Mean = 5.9 Anxious-spaced: Mean = 7.9 The data is analysed with a regression model using effects coding, where x1 codes emotional state (1 = calm, -1 = anxious), and x2 codes for study type (1 = massed, -1 = spaced). You run your model as: performance ~ emotion + studytype + emotion*studytype What is the b2 term? Answer to 2 decimal place in the form X.XX - answer--1.05 Imagine a 2x2 interaction plot. IV1 is plotted on the x-axis, IV2 is denoted by two lines. If the two lines denoting IV2 have the same slope, you'd likely infer... - answer-There is no interaction. . Remember that an interaction plot indicates an interaction when the slopes of the lines denoting different levels of the IV denoted by lines are different from one another (i.e., the lines are non-parallel). I have a 5x3 factorial design. How many coefficients will my full model have to represent each categorical variables and all interaction terms? - answer-14 I have a factor in R called `study_group` as one variable in my dataset (called `df`). `study_group` has 4 levels. I want to code this factor so that when included in an lm() model, it provides me with effects codes. Which of the following is the correct code to do this? - answer-contrasts(df$study_group) - (4) I run the following model including dummy variables for a 3-level factor (Group 1 = reference; D1 = coded 1 for group 2, 0 otherwise; D2 = coded 1 group 3, 0 otherwise) and a continuous covariate (X1). True of false b1 is the mean difference between Group 1 and group 2 adjusted for X1? - answer-True I run the following models: m1 - lm(DV ˜ Group, data = df) m2 - lm (DV ˜ Group + cov, data = df) anova(m1, m2) The resultant test from anova() gave me a p-value of 0.63. What does this mean? - answer-The inclusion of cov did not significantly reduce the residuals sums of squares. True or False: The F-test for the main effect of a experimental condition in a one-way ANOVA is the same as the model F-test for the linear model containing dummy or effect coded variables representing the experimental condition? - answer-True