please answer all thanks!QUESTION 2a.b.C.Show that the regression R² in the regression of Y on X is the squared value of thesample correlation between X and Y. That is, show that R² = r²XY.Show that the R² from the regression of Y on X is the same as the R² from theregression of X on Y.Consider the regression model Y₁ - Bo + B₁X₁ + 14a. Suppose you know that Bo= 0. Derive a formula for the least squares estimator ofB₁.b. Suppose you know that Bo= 4. Derive a formula for the least squares estimator ofB₁.

Answered: QUESTION 2 a. b. C. Show that the…

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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1. The Gross Horsepower of a car can influence the mileage of the car. A random sample of 32 different cars’ Gross Horsepower and mileage (Miles/gallon) is collected. From the data, suppose you got the following results: Pearson’s correlation coefficient: -0.90 The fitted regression line: Ŷ = 30. 10 − 0. 07 X d. Find the value of R2 and comment. e. From the fitted model find the values of Y for given values of X as 110. How do you interpret this value?
Which of the following four statements is correct?Note: Only one answer is correct per question.1) Let f (x) = 2 + 5x be a linear regression line of a linear regression from Y to X.Then the following applies to the scatter plot: 1) The closer the points in the scatter diagram to the regression line drawnthe stronger the correlation between X and Y. 2) The further the points in the scatter plot are from the regression line drawn away, the stronger the correlation between X and Y. 3) Only if all points lie exactly on the regression line drawn isthe correlation between X and Y is strong. 4) The position of the points in the scatter plot has nothing to do with the strength of the correlation. 2) For the events A = "number of points when rolling the dice is two" and B = "number of points when rolling the diceRolling the dice is straight ":* P (A \ B) is smaller than P (A).* P (A \ B) is the same size as P (A).* P (A \ B) is greater than P (A).* No general statement can be made about…
What is the value of r2? Use the square root and your knowledge about the slope of the regression line to find the value of the correlation constant r. Based only on the value of r, do you think this line is useful for predicting life expectancy from the infant mortality rate? A new country called Arendelle has formed and has an infant mortality rate of 42 (deaths per 1000 live births). Use the equation of the regression line to predict the life expectancy for Arendelle. Round your answer to one decimal place. Another new country called Weselton has formed and has an infant mortality rate of 250 (deaths per 1000 live births). Recall some of the cautions we should take when considering correlation. In one or two complete sentences, explain why using the linear regression equation to make a life expectancy prediction is not a good idea for Weselton. If you had to choose exactly one potential influential outlier from the original data set, what would it be? Identify the point as an…
Suppose you are interested in studying the relationship between the number of visitors a museum gets and the revenue of their gift shop. You take a sample of 27 different days and record the number of visitors and the revenue of the gift shop in dollars. Also suppose on the 27 days you sampled, the number of visitors ranged from 100 people to 600 people. You get the following regression line: ŷ = 5.6x419, where ŷ is the revenue in dollars and x is the number of visitors. We also get that r≈.57. (a) Give the value of the slope of this regression line. Interpret this value in the context of the situation. (b) Is there enough evidence for a correlation? Why or why not? (c) What does our model predict the revenue will be on a day where the museum gets 1000 visitors? Would you trust this prediction? Why or why not? (d) Suppose that the first day we visited the museum it had 220 visitors and made a revenue of 780 dollars. Calculate the residual for this data point. Make sure to include…
Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below. Hours spent studying, x D Test score, y Test score 80- 0- E Hours studying Q 0 39 Find the regression equation. ŷ=x+ X (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) Choose the correct graph below. OA. G 2 44 OB. 3 50 Test score 80- #R 0 3 48 Hours studying (a) Predict the value of y for x=2. Choose the correct answer below. OA. 49.8 OB. 47.0 OC. 55.5 OD. not meaningful (b) Predict the value of y for x=3.5 Choose the correct answer below. 4 65 Q 6 70 wwx O C. Test score 80+ (a) x=2 hours (c) x = 15 hours 8 Hours studying Q Q O D. 80- (b)x= 3.5…
You are given below the following information about advertising and sales. Adv. Exp. (X) (S Lakhs) Sales (Y) Lakhs) Мean 10 90 S.D. 3 12 Correlation Coefficient 0.8 (a) Calculate the two regression lines. (b) Find the likely sales when advertisement expenditure is (c) What should be the advertisement expenditure if the company wants to attain a sales target of 15 lakhs. 120 lakhs ?
I just need help on on parts H, i and J. The regression line for part G is on the first page. Thank you.
The following table gives the data for the average temperature and the snow accumulation in several small towns for a single month. Determine the equation of the regression line, ŷ = bo + b₁x. Round the slope and y-intercept to the nearest thousandth. Then determine if the regression equation is appropriate for making predictions at the 0.05 level of significance. Critical Values of the Pearson Correlation Coefficient Average Temperature (°F) Average Temperatures and Snow Accumulations 42 31 24 45 38 18 33 21 25 9 12 27 7 15 22 30 13 20 37 Snow Accumulation (in.) 8
The following table shows students’ number of absences, x, and the student’s final grade,, y.# of absences x 6 2 15 9 12 5 8 Final grade y 82 86 43 74 58 90 78a) Calculate r, the correlation coefficient ________________b) Find the equation of the regression line __________________________________c) If a student is absent 4 times,, what grade does your regression line predict?__________________

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