25/ A: Use Linear Regression to fit the following experimental data
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Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 6 Y 4 6. 10 10 8
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Q: Q5/ Use Linear Regression to fit the following data: 2 3 4 5 6 Y 4 9 10 10 9 8 3
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A: Please find the explanation below.
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Q: Q5/ Use Linear Regression to fit the following data: 2 10 1 4 5 6 Y 4 10 9 3
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Q: Q5/ Use Linear Regression to fit the following data: 2 4 5 6. Y 4 9 10 10 8
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Q: 1 2 3 4 5 6 Y 4 10 10 8 3
A: Here follow the python code.
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- If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?The model developed from sample data that has the form of Yhat = bo +bjX is known as the multiple regression model with two predictor variables. (True or False) O True O FalseInterpret the least squares regression line of this data set. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The correct least squares regression line for the data set is: y = 8.116x + 273.273 Use it to complete the following sentence: The least squares regression line predicts an additional annual rainfall if the average temperature of coastal waters increases by one degree millimetres of Celsius.
- FRQ 2 Professional basketball teams have 11 players per team. Salary is dependent upon their scoring average, measured in points per game. A least-squares regression line that describes the relationship between scoring average and salary for one professional basketball team is ŷ = 2,671,134.68 +684,663.08x, where x is the player's scoring average and y is the player's salary. The residuals for this regression are given in the graph below. Residual $20,000,000 $15,000,000 $10,000,000 $5,000,000 $0 -$5,000,000 -$10,000,000 -$15,000,000 4 ITS % 6 MacBook Pro ● 8 ● ● ● 10 12 14 Scoring Average (Points per Game) Is a line an appropriate model to use for these data? What information tells you this? b) What is the value of the slope of the least-squares regression line? Interpret the slope in the context of this problem. c) What is the predicted salary of the basketball player with 10.9 points per game? d) Approximate the actual salary of the basketball player with 10.9 points per game. 16 tv…A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study) to be used for predicting te For a person who studies for 2 years, obtain the 95% prediction interval and write a statement interpreting the interval. (42.72, 63.98); We can be 95% confident that the test score of an individual who studies 2 years will lie in the interval (42.72, 63.98) (31.61, 75.09); We can be 95% confident that the test score of an individual who studies 2 years will lie in the interval (31.61, 75.09) (42.72, 63.98); We can be 95% confident that the mean test score of all individuals who study 2 years will lie in the interval (42.72, 63.98) (31.61, 75.09); We can be 95%…Suppose we are given a least squares regression line ˆy= 4.3x +10. If a data point used to obtain the regression line is (1.5, 16) then the residual at that point is which of the following: (i) 0.45 (ii) -0.45 (iii) 0.55 (iv) 16.45
- Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ?X is the age of the crab in months and ?ˆY^ is the predicted value of ?Y, the size of the male crab in cm. ?ˆ=9.1367+0.4817��Y^=9.1367+0.4817X What is the value of ?ˆY^ when a male crab is 22.1725 months old? Provide your answer with precision to two decimal places.The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year’s usage and temperatures are in the following table: Assuming that a simple linear regression model is appropriate, fit the regression model relating stem usage (y) to the average temperature (x). What is the estimate of Sigma2? What is the estimate of expected stem usage when the average temperature is 55 F? What change in mean stem usage is expected when the monthly average temperature changes by 1 F? Suppose that the monthly average temperature is 47 F. Calculate the fitted value of y and the corresponding residual. Test for significance of regression using α=0.01 (Use ANOVA). Calculate the r2 of the model. Find a 99% CI for B1 .Plot the linear regression line y = 3 + 0.5x without using excel with proper labelling
- What types of independent variables—binary or continuous—may interactwith one another in a regression? How do you interpret the coefficient on theinteraction between two continuous regressors and two binary regressors?A study was done to determine whether or not social exclusion causes “real pain.” Researchers looked at a random sample of 7 individuals and measured brain activity in an area of the brain that responds to physical pain to see if activity increases as distress from social exclusion increases (measured by social distress score). The social distress scores in the experiment ranged from 0 to 10. A scatterplot shows a moderately strong linear relationship. The least squares regression line is has a slope of 0.06078 and an intercept of -0.1261. A person has a social distress score of 2.0 and a brain activity level of 0.15. What is their residual?Consider the model Ci= B0+B1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950. The number of degrees of freedom for this regression is A. 2950 OB. 2948 OC. 2952 OD. 2
