PSY 10 Assignment 8 of 8, One of 8 assingments completed in Lab PDF

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Over the course of this class, we were required to complete 8 labs that related to course material and use of the program R studio....

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PSY 10B - Statistics Fall 2021 Assignment 8

DIRECTIONS Total Points = 25

PART I 1. Compare and contrast the information that we get from a correlation coefficient compared to the information that we get when we use the equation for a straight line in regression. Think about how the two are similar as well as what extra we can do with regression that we cannot do with correlation. (1 point) Both correlation coefficients and straight line regressions demonstrate the direction and strength of the relationship between two continuous variables: X and Y respectively. Correlation coefficients can only assess the relation between X and Y. Straight line regression analysis, in contrast, allows researchers to use information from the predictor (x) variable to make predictions about the outcome (y) variable.

2. The simple linear regression equation is: Ŷ = a + bx. Identify and describe each part of the regression equation. (Hint. For full points make sure that you describe or give a definition for each part of the regression equation.) (2 points) o o o o

Ŷ --> predicted value of outcome (criterion) variable X --> value of predictor variable b --> slope of the regression line (tells us about direction and strength)  Steeper slope = stronger relation a --> y intercept, value of y hat when x = 0

3. Imagine that you are contemplating on whether or not you want to go to graduate school for psychology. One factor that will determine whether or not you choose to go is how much extra money you can earn as a psychologist by gaining extra schooling. You decide to collect some data to help you make your decision. You interview 20 psychologists and obtain the following information: (6 points total) Years of School M = 16 SD = 5

Income M = 55k SD = 10k r = .62

a.

Calculate the b (slope) for the regression equation. What does this value mean in the context of the data (Hint. Think about what the slope tells you regarding how much more money you can make (in $1,000 increments) by gaining one extra year of education.)? (2 points) b=

r x , y∗s y sx

= 0.62 (

10 ) = 1.24 5

b. Calculate the a (intercept) in the regression equation. What does this value mean in the context of the data (Hint. Think about what the intercept tells you regarding the regression line and the y-axis on a scatterplot.)? (2 points) a=

c.

M y −b∗M x = 55 – (1.24)(16) = 35.16

Write out the regression equation (1 point) Ŷ =35.16 + 1.24x

d. If you decide to go to graduate school to get a PhD, you will have 20 years of education. How much money are you predicted to make based on the regression equation above? Show your work. (1 point) Ŷ =35.16 + 1.24(20) = 35.16 +24.8 = 59.96k/year

4. Below is a scatterplot with the regression line inserted. Use this scatterplot to answer the following questions. They are conceptual questions; you do not need to calculate anything. You can use the same scatterplot to answer all of the parts below, or if it seems too crowded or unclear to put everything on one plot, just copy and paste a new one for each part below. Either way is fine. Just make sure that it is clear. (3 total points)

a. On the scatterplot, draw where the SSresidual is coming from conceptually. Make sure that it is clearly labelled on the figure. (Note. You do not have to draw every instance of where the SSresidual would be coming from, just enough or a few examples to let us know that you understand.) (1 point)

b. Imagine that the MY = 3.00. On the scatterplot, draw where the SSregression is coming from conceptually. Make sure that it is clearly labelled on the figure. (1 point)

c. Imagine that the MY = 3.00. On the scatterplot, draw where the SSTotal is coming from conceptually. Make sure that it is clearly labelled on the figure. (Note. You do not have to draw every instance of where the SStotal would be coming from, just enough or a few examples to let us know that you understand.) (1 point)

PART II 5. Conduct a simple linear regression to explore whether pro-environmental actions predict beliefs about climate change. (2 points) a. Paste the R code below. (1 point) r1|t|) (Intercept) 2.39861 0.15134 15.850 < 2e-16 *** enviro_action 0.30646 0.05465 5.607 6.42e-08 *** --Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.5165 on 210 degrees of freedom Multiple R-squared: 0.1302, Adjusted R-squared: 0.1261 F-statistic: 31.44 on 1 and 210 DF, p-value: 6.42e-08

6. Conduct a multiple linear regression to explore whether pro-environmental actions, age, and education all predict beliefs about climate change. (2 points) a. Paste the R code below. (1 point) r1|t|) (Intercept) 2.3537188 0.2123015 11.087 < 2e-16 *** enviro_action 0.3056667 0.0549647 5.561 8.18e-08 *** Age 0.0008412 0.0033771 0.249 0.804 Education 0.0046215 0.0283366 0.163 0.871 --Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.5189 on 208 degrees of freedom Multiple R-squared: 0.1306, Adjusted R-squared: 0.1181 F-statistic: 10.42 on 3 and 208 DF, p-value: 2.046e-06

7. Look back at the R2 for the two outputs that you have above (the simple and multiple linear regression). Describe what R2 is conceptually (Hint. Look back to the formula). Then, compare what the two R2 are telling you about the data and how they are different. (2 SS regression 2 points) R = SS y 2 R represents a percentage of total variability accounted for by the regression line. From the simple linear regression, R2 = 0.1302. This means that 13% of the variation in climate change belief is accounted for by pro-environmental actions. In contrast, the R2 value (0.1306) produced by the multiple linear regression represents the amount of variance accounted for by all of the predictors together as a percentage of total variability. Thus, we can say that 13% of the variation in climate change belief is accounted for by proenvironmental action, age, and education.

8. Interpret the regression analyses for the simple linear regression that you conducted above using APA style. [Hint. Make sure to interpret the results in the context of the study. Use the slide in the lab section to make sure that you have all of the components in the interpretation.] (7 points) A simple linear regression analysis was conducted: the predictor was environmental action and the outcome (criterion) was climate change belief. There was a significant effect: engagement in proenvironmental action accounts for 13% ( R2 ¿ of the variance in climate change belief. F(1,210) = 31.44, p = 6.42e-08. Specifically, as pro-environmental action increases by one unit, climate belief increases by b = 0.31, t(210) = 5.607, p = 6.42e-08. Thus, we may say that a positive relationship exists between pro-environmental action and climate belief. This means that individuals who engage in pro-environmental action are more likley to believe in climate change....