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Is high school GPA a good predictor of college GPA? Let's explore it with some real data. In RStudio, run the following code to install and/or library the package "openintro". 1. install.packages("openintro") # don't do this again if you already did this! 2. library(openintro) 3. satgpa Delete the install line of code if you are in an RMD file so that it doesn't install every time you knit. The last line of code will access the dataset of that name. The dataset 'satgpa' gives information about test scores and GPA in high school and college for students at an unnamed college. Use the data to build a model to predict first year college GPA ("fy_gpa") from high school GPA ("hs_gpa"). a. Make a scatterplot of "fy_gpa" (y-axis) vs "hs_gpa" (x-axis). Which plot is the scatterplot? Graph A Graph B Graph C Graph D

Is high school GPA a good predictor of college GPA? Let's explore it with some real data. In RStudio, run the following code to install and/or library the package "openintro". 1. install.packages("openintro") # don't do this again if you already did this! 2. library(openintro) 3. satgpa Delete the install line of code if you are in an RMD file so that it doesn't install every time you knit. The last line of code will access the dataset of that name. The dataset 'satgpa' gives information about test scores and GPA in high school and college for students at an unnamed college. Use the data to build a model to predict first year college GPA ("fy_gpa") from high school GPA ("hs_gpa"). a. Make a scatterplot of "fy_gpa" (y-axis) vs "hs_gpa" (x-axis). Which plot is the scatterplot? Graph A Graph B Graph C Graph D

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Is high school GPA a good predictor of college GPA? Let's explore it with some real data. In RStudio, run the following code to install and/or library the package "openintro". 1. install.packages ("openintro") # don't do this again if you already did this! 2. library(openintro) 3. satgpa Delete the install line of code if you are in an RMD file so that it doesn't install every time you knit. The last line of code will access the dataset of that name. The dataset 'satgpa' gives information about test scores and GPA in high school and college for students at an unnamed college. Use the data to build a model to predict first year college GPA ("fy_gpa") from high school GPA ("hs_gpa"). a. Make a scatterplot of "fy_gpa" (y-axis) vs "hs_gpa" (x-axis). Which plot is the scatterplot? Graph A Graph B Graph C Graph D O A C₁- fy_gpa hs_gpa b. Does the relationship appear roughly linear? O No, all the points do not fall on a straight line. O Yes, there is no obvious curvature in the graph O No, there are gaps in the graph along the x-axis. Yes, all the points fall on a straight line. Ho: #1 = 0.743 HA: 10.743 c. Do the data provide strong evidence that high school GPA and first-year college GPA are associated? State the null and alternative hypotheses, report the p-value, and state your conclusion. i. The hypotheses are: Ho: 21=0 HA: 2₁0 Ho: 8₁ 0 Ηλ: β. > 0 Ho: B₁=0 HA: B₁0 hs_gpa hs_gpa iii. The result of this hypothesis test is: ⒸH₂ : ₁ = 0 H₁:10 ii. The p-value for the test is (round to three decimal places--if that value is 0 then enter 0.): Ho: B₁ 0.743 HA: B₁ 0.743 e. What is the equation of the regression line? OGPA coll -0.091 GPA +0.743 OGPA -0.743 GPAcoll+ 0.091 OGPA coll 0.743 GPAhs+ 0.091 OGPA -0.091 GPA coll +0.743 About 29.5% of the variation in first-year college GPA is explained by the least-squares line. O high school GPA is predictive of first-year college GPA. About 29.5% of the variation in high school GPA is explained by the least-squares line. O high school GPA is not predictive of first-year college GPA. d. Interpret R². O the amount of variation in first-year college GPA that is explained by the least squares line. The total amount of variation in the model. O The total unexplained variation in the model. O The amount of variation in high school GPA that is explained by the least squares line. f. Interpret the slope in the context of the model. For each Select an answer V increase in Select an answer Select an answer Select an answer Select an answer g. Interpret the y-intercept in the context of the model or explain why it should not be interpreted. When the first-year college GPA of a student is 0 the expected value of high school GPA is 0.091. When the first-year college GPA of a student is 0 the expected value of high school GPA is 0.743. When the high school GPA of a student is 0 the expected value of first-year college GPA is 0.091. O It does not make sense to interpret the y-intercept for this model because no student in the data had a high school GPA anywhere close to 0.
Transcribed Image Text:Is high school GPA a good predictor of college GPA? Let's explore it with some real data. In RStudio, run the following code to install and/or library the package "openintro". 1. install.packages ("openintro") # don't do this again if you already did this! 2. library(openintro) 3. satgpa Delete the install line of code if you are in an RMD file so that it doesn't install every time you knit. The last line of code will access the dataset of that name. The dataset 'satgpa' gives information about test scores and GPA in high school and college for students at an unnamed college. Use the data to build a model to predict first year college GPA ("fy_gpa") from high school GPA ("hs_gpa"). a. Make a scatterplot of "fy_gpa" (y-axis) vs "hs_gpa" (x-axis). Which plot is the scatterplot? Graph A Graph B Graph C Graph D O A C₁- fy_gpa hs_gpa b. Does the relationship appear roughly linear? O No, all the points do not fall on a straight line. O Yes, there is no obvious curvature in the graph O No, there are gaps in the graph along the x-axis. Yes, all the points fall on a straight line. Ho: #1 = 0.743 HA: 10.743 c. Do the data provide strong evidence that high school GPA and first-year college GPA are associated? State the null and alternative hypotheses, report the p-value, and state your conclusion. i. The hypotheses are: Ho: 21=0 HA: 2₁0 Ho: 8₁ 0 Ηλ: β. > 0 Ho: B₁=0 HA: B₁0 hs_gpa hs_gpa iii. The result of this hypothesis test is: ⒸH₂ : ₁ = 0 H₁:10 ii. The p-value for the test is (round to three decimal places--if that value is 0 then enter 0.): Ho: B₁ 0.743 HA: B₁ 0.743 e. What is the equation of the regression line? OGPA coll -0.091 GPA +0.743 OGPA -0.743 GPAcoll+ 0.091 OGPA coll 0.743 GPAhs+ 0.091 OGPA -0.091 GPA coll +0.743 About 29.5% of the variation in first-year college GPA is explained by the least-squares line. O high school GPA is predictive of first-year college GPA. About 29.5% of the variation in high school GPA is explained by the least-squares line. O high school GPA is not predictive of first-year college GPA. d. Interpret R². O the amount of variation in first-year college GPA that is explained by the least squares line. The total amount of variation in the model. O The total unexplained variation in the model. O The amount of variation in high school GPA that is explained by the least squares line. f. Interpret the slope in the context of the model. For each Select an answer V increase in Select an answer Select an answer Select an answer Select an answer g. Interpret the y-intercept in the context of the model or explain why it should not be interpreted. When the first-year college GPA of a student is 0 the expected value of high school GPA is 0.091. When the first-year college GPA of a student is 0 the expected value of high school GPA is 0.743. When the high school GPA of a student is 0 the expected value of first-year college GPA is 0.091. O It does not make sense to interpret the y-intercept for this model because no student in the data had a high school GPA anywhere close to 0.
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