A producer of educational TV shows for gifted children wants to promote the claim that gifted children'sscores on an analytical test increase the more the children watch their shows.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. giftedDelete the install line of code if you are in an RMD file so that it doesn't install every time you knit. Thelast line of code will access the dataset of that name.dataset named gifted gives information about test scores of gifted children on a standard analyticalThetest and the number of hours of educational TV these children watch. use the data set to make a model topredict score on analytical skills test (score") from hours of educational TV watched per week (edutv").a. Make a scatterplot of "score" (y-axis) vs "edutv" (x-axis). Which plot is the scatterplot?Graph A Graph B Graph C Graph DoỏA1954180C₁-13dutyedutyb. Does the relationship appear roughly linear?O No, all the points do not fall on a straight lineYes, there is no obvious curvature in the graphYes, all the points fall on a straight line.✔Right!O No, there are gaps in the graph along the x-axis.✓✔Right!DⒸH₂ : 3₁-0H₁:3₁ 0H₂:23.067195HA: 3.0671801c. 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.1. The hypotheses are:✔Right!ⒸH₂:30H₁:0ⒸH₂:21 = 0H₁:10III. The result of this hypothesis test is:✔Right!editv11. The p-value for the test is (round to three decimal places if that value is 0 then enter 0.):eduty24e. What is the equation of the regression line?Ohoursry 165.144 score 3.067O hoursy -3.067 score 165.144O score 165.144 hoursry-3.067score -3.067 hoursyy 165.144✓ⒸH₂:₁-0H:0About 13.71% of the variation in hours of educational TV watched per week is explainedby the least squares line.O hours of educational TV watched per week is not predictive of score on analytical skillstest.ov✔Right!Ho: 13.067HA:B 3.067hours of educational TV watched per week is predictive of score on analytical skills test.About 13.71% of the variation in score on analytical skills test is explained by the leastsquares line.d. Interpret ²O The amount of variation in hours of educational TV watched per week that is explained by thewwwwleast squares linef. Interpret the slope in the context of the model.Select an answerSelect an answerSelect an answerthe amount of variation in score on analytical skills test that is explained by the least squaresline.The total amount of variation in the modelO The total unexplained variation in the model.For each Select an answer].[Select an answerZincrease in8. Interpret the y-intercept in the context of the model or explain why it should not be interpreted.When the score on analytical skills test of a gifted child is 0 the expected value of hours ofeducational TV watched per week is -3.067.When the score on analytical skills test of a gifted child is 0 the expected value of hours ofeducational TV watched per week is 165.144.It does not make sense to interpret the y-intercept for this model because no gifted child inthe data had a hours of educational TV watched per week anywhere close to 0When the hours of educational TV watched per week of a gifted child is 0 the expected valueof score on analytical skills test is 165.144

In this question we want to study the relationship between the independent variable "educational TV watched per week" and the dependent variable "score on analytical test".The commands to load the data set in R and further calculations performed are as follows: install.packages("openintro")library(openintro) data(gifted)summary(gifted) y <- gifted$scorex <- gifted$edutv plot(x, y, type = "p", xlab = "edutv", ylab = "score") model <- lm(y~x)summary(model) The output is as follows:a) The plot is as follows: The scatterplot matches option A. Answer: Graph Ab) According to the scatterplot, there is large variability within the points as visible from the scatterplot. Hence, the relationship between the two variables is weak. Answer: D c) Consider a simple linear regression model: y=β0+β1x+ε To test whether x and y are associated significantly or not, we test the significance of the slope of the model. i. The hypothesis is as follows: H0: β1=0H1: β1≠0 ii. From the summary of the model, the p-value is 0.026 iii. As p-value < 0.05, we may reject the null hypothesis at 5% level of significance and conclude that there is significant association between score and edutv. Answer: Bd) The coefficient of determination R2 explains the amount of variation in the dependent variable which is explained by the independent variable. Answer: B e) From the output of the regression in R, we have: intercept = 165.144 slope = -3.067 The regression line is as follows: score^=165.144-3.067 hoursTV Answer: D f) For each one hour increase in the number of hours TV was watched (hoursTV), the gifted children's scores on an analytical test decrease by 3.067 g) The intercept of the model is interpreted as follows: When hoursTV is 0, the expected score on the test is 165.144 Answer: D