**3. A Simple Regression Problem****(a)** Find point estimates for α, β, and σ².In this section, students are expected to determine the point estimates for the parameters α (alpha), β (beta), and σ² (sigma squared) in the context of a simple linear regression problem. These point estimates are typically derived using statistical methods such as Ordinary Least Squares (OLS). ### Data Table for AnalysisBelow is a dataset presented in two columns, \( X \) and \( Y \), each containing numerical values. The dataset can be utilized for various statistical analyses such as correlation, regression, and trend analysis. #### Data Values:| **X** | **Y** ||:--------:|:--------:|| 5 | 16.1 || 5 | 17.4 || 5 | 18.7 || 9 | 25.9 || 7 | 20.3 || 5 | 16.1 || 6 | 18.2 || 10 | 32.1 || 5 | 17.3 || 6 | 21.6 || 7 | 20.9 || 5 | 15.9 || 5 | 14.2 || 9 | 28.1 || 8 | 23.2 || 4 | 14.8 || 6 | 19.7 || 6 | 19.0 || 7 | 22.8 || 5 | 17.9 || 5 | 16.3 || 10 | 27.9 || 8 | 22.6 || 5 | 16.8 || 8 | 24.1 |#### Interpreting the Data:This dataset can be plotted on a graph to visually examine the relationship between the \( X \) and \( Y \) variables. For example, a scatter plot will help reveal patterns, trends, or correlations. Statistical tests can be applied to determine if the relationship between \( X \) and \( Y \) is significant. The repeated values for \( X \) and their corresponding \( Y \) values suggest that there may be an underlying pattern or other factors

Introduction: The response variable here is y, and the explanatory variable is x. The population…

Answered: A Simple Regression Problem (a) Find…

Math

Statistics

A Simple Regression Problem (a) Find point estimates for a, B, and o?.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Complete the statements. The sign of the correlation coefficient and the sign of the slope of the regression line will... 1. always be the same 2. sometimes be the same 3. always be different When r is positive, b... 1. will be positive 2. may be positive 3.will be negative When r is negative, b... 1. will be positive 2. may be positive 3.will be negative
3. Use the following data to determine which factor is most predictive of test scores. For each independent variable, create a scatterplot for its relationship with test scores. Also calculate Pearson's r for each variable. Based on the scatterplot and Pearson's r, which factor has the strongest relationship with test scores? Student ID Test Score Sleep Hrs. Studied IQ GPA 1 67 6.5 4 90 2.9 2 77 8.5 7 102 2.8 3 96 7.5 16 130 3.8 4 61 5 93 2.2 5 89 11 125 3.1 6. 73 5 106 2.4 7 93 8 17 122 3.4 8. 58 5.5 2 88 1.7 75 100 2.4 10 82 10 8 107 3.0 11 90 12 14 118 3.6 12 69 11 3 92 2.0 13 84 7.5 9 103 3.2 14 78 6.5 13 77 2.8 15 63 2 2 99 2.5 16 87 114 3.3 17 76 8 8 110 2.4 18 70 11.5 1 125 2.8 19 72 10 4 86 2.1 20 50 70 1.5 ON 05
A researcher wants to explore the relationship between two variables: Time 1 and Time 2. Time 1 421 390 459 384 403 Time 2 A. O Matched pairs B. O Inference for regression C. O Two independent samples 400 383 436 362 392 A group of student athletes was training for an obstacle course event by practicing a variety of exercises. Their coach wanted to know if the exercises were in fact related to their time to complete the obstacle course. Time 1 was each athlete's time (in seconds) for 20 repetitions of shuttle runs (running back and forth between 2 cones placed 25 meters apart) during training. Time 2 was the same athlete's time (in seconds) to complete the obstacle course during the competition. If the coach wants to see if there was an association between time to complete 20 shuttle runs during training (in seconds) and the time to complete the obstacle course during competition (in seconds), which of the following is the appropriate inference method to analyze these data?
2. Interesting data are given as: X Y72 4573 3875 41 76 3577 3178 4079 2580 3280 3681 2982 3483 3884 2685 3286 2888 27 Compute thea. Correlation Coefficient r b. The regression.
Annual Income. The Census Bureau collects data on income by educational attainment, sex, and age. Results are published in Current Population Reports. From a random sample of 75 males between the ages of 25 and 50, all of whom have at least a ninth-grade education, data were collected on age, number of years of school completed, and annual income. We performed a multiple regression analysis for annual income (in thousands of dollars) with the variables age and number of years of school completed as predictor variables. The resulting output is shown in Output A.21. a. Use the computer output to obtain the regression equation for annual income in terms of age and number of years of school completed. b. Apply the regression equation to predict the annual income of a male who is 32 years old and has completed exactly 4 years of college (i.e., 16 years of school). c. Find and interpret the coefficient of determination, R2 d. Find and interpret the standard error of the estimate. e. At the…
The following table shows the annual family income of the students enrolled in the JRMSU-TC and their general weighted average (GPA). Students Annual Family Income (Pesos) General weighted average (GPA) % 1 85 100,000 50,000 2 79 3 150,000 180,000 5 300,000 6 500,000 7 230,000 1. Plot the regression line with the data. 2. Discuss the results. 34 82 85 93 92 95
Name Abhu Keit Carli Danni Ek Liang Ramone Age 1 3 6 9 10 11 12 Show size 1 4 7 6 9 9 1 Consider the table if data above: 1) After performing a linear regression analysis, what is the equation of the line of best fit? State the letter of the correct answer. a) shoe size= -0.81 x Age + 0.85 b) shoe size= 0.81 x Age - 0.85 c) shoe size= 0.81 x Age + 0.85 d) shoe size= 0.85 x Age + 0.81
Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks. Dolphin Number of Treats Number of Attempts Diana 2 5 Frederick 4 4 Fatima 1 7 Marlin 3 4 You can use the preceding sample data to obtain the regression line, where Ŷ is the predicted value of Y: ŶŶ = = bX + abX + a One formula for the slope of the regression line is as follows: bb = = SPSSxSPSSx To calculate the slope, first calculate SP and SSxx: SP = , and SSxx = . (Hint: For SP use the computational formula and for SSxx use the definitional formula.) The slope of the regression line is , and the Y intercept of the regression line is . The difference between Y and Ŷ for a…
The overall purpose of regression analysis is: a) to lessen our error in making predictions b) to make perfect predictions, since all data points mustfall on the regression line c) to exploit the correlation between Y and X and use it to help make better predictions of Y d) two of the above e) three of the above f) none of the above
6.In simple linear regression, the sample correlation coefficient between the input variable and the output variable, and the estimated slope parameter : a.Must have the same sign (negative, zero, or positive) b.May have opposite signs c.Must have opposite signs d.Neither of the above
need help. please
Part #2