To examine whether there is any association between the performances on the twotests, T1 and T2 (test T1 was conducted before T2), and whether T2 scores could bepredicted in terms of T1 scores. A random sample of 150 students in Statistics majorwas selected. Let the scores be denoted S1 and S2 for tests T1 and T2, respectively.The tests had different maximum points. The following outputs using R codes wereobtained.fit<-lm (S2~S1)summary(fit)onCall:Im (formula = S2 *S1)20253035404550Residuals:Score: S1Min1QMedian3QМаx-13.0214-3.09340.29522.937914.5996Coefficients:Estimate Std. Error t value Pr(>[t])(Intercept) 0.101522.510030.040.968S10.267230.0192113.91<2e-16 ***Signif. codes:O ***' 0.001 **' 0.01 (*' 0.05 '.' 0.1 '? 1Residual standard error: 4.472 on 148 degrees of freedomMultiple R-squared:F-statistic: 193.6 on 1 and 148 DF,0.5667, Adjusted R-squared:0.5638p-value: < 2.2e-16plot (fit$fitted,fit$residuals, xlab="fitted values", ylab="residuals")qqnorm (fit$residuals)Normal Q-Q Plotoo000000O Go agod0000 0.of2530354045-22fitted valuesTheoretical Quantilesesiduals15Score:Sample Quantiles091 Justify your answers and show calculations, if any.(i)Is a linear relationship between Si and S2 appropriate? Justify your re-sponse.(ii)Is the role of S1 significant in predicting S2, at a = 0.001?(i)What is the sample correlation between S1 and S2?

(i) From the given output it can be observed that the scatterplot for the two variables is following…

Answered: Justify your answers and show…

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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Q 1 If X is a random variable with distribution X: 0 1 2 3 P(X): 1111 44 44 Find the mean, Variance and standard deviation. Q 2 If X is a random variable with distribution X: 0 12 3 4 P(X): 0 K 2K 3K 4K Explain the following: (i) For which value of K, P(X) is probability mass function? (ii) Find the following probabilities: (a) P(1 ≤ X < 4). (b) P(2 < X < 4). Q3 A box contains 6 balls. Two are numbered 4, two are numbered 5, and two are numbered 6. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the variance (²) and standard deviation (o) of the numbers on the balls. Q4 A special six-sided die is made in which 2 sides have 6 spots, 3 sides have 4 spots, and 1 side has 1 spot. If the die is rolled, find the expected value of the number of spots that will occur. Q5 Let X-B(4,0.6). Find the following (i) P(X = 2) (ii) P(1 < X < 4) (iii) Also find mean and variance. Q6…
A random sample of college students was surveyed about how they spend their time each week. The scatterplot below displays the relationship between the number of hours each student typically works per week at a part- or full-time job and the number of hours of television each student typically watches per week. The correlation between these variables is r = –0.63, and the equation we would use to predict hours spent watching TV based on hours spent working is as follows: Predicted hours spent watching TV = 17.21 – 0.23(hours spent working) Since we are using hours spent working to help us predict hours spent watching TV, we’d call hours spent working a(n) __________________ variable and hours spent watching TV a(n) __________________ variable. The correlation coefficient, along with what we see in the scatterplot, tells us that the relationship between the variables has a direction that is _________________ and a strength that is ______________________. According to the…
The scatterplot below shows the relationship between two random variables X and Y. (a) Is the correlation a good metric for describing the relationship between X and Y for these data? Why or why not? Regardless of your answer suppose you calculated the sample correlation between X and Y and found that r = -0.15. Explain in one sentence what this means. (b) If, as noted in (a), r = -0.15 then what is the value of the correlation between 2X and 5Y? (c) Based on (b) draw your best approximation to the least squares regression line that fits the data above. Also, make a rough sketch of the corresponding residual plot.
You run a regression analysis on a bivariate set of data (n = 120). With i = 66.3 and y = 50.6, you obtain the regression equation y = 4.097x – 11.636 with a correlation coefficient of r = 0.56. You want to predict what value (on average) for the response variable will be obtained from a value of 120 as the explanatory variable. What is the predicted response value? y = (Report answer accurate to one decimal place.)
3. Regression analysis breaks scores on the DV into... (explain and give equations)
Given the correlation coefficient 0.794 and the linear regression equation ŷ = 16.4 +1.58x, compute the coefficient of determination. p² Round to 4 decimal places. =

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Justify your answers and show calculations, if any. (i) Is a linear relationship between S1 and S2 appropriate? Justify your re- sponse. (ii) Is the role of S1 significant in predicting S2, at a = 0.001? (iii) What is the sample correlation between S1 and S2?