Suppose a local university researcher wants to build a linear model that predicts the freshman year GPA of incoming studentsbased on high school SAT scores. The researcher randomly selects a sample of 40 sophomore students at the university andgathers their freshman year GPA data and the high school SAT score reported on each of their college applications. Heproduces a scatterplot with SAT scores on the horizontal axis and GPA on the vertical axis. The data has a linear correlationcoefficient of 0.481202. Additional sample statistics are summarized in the table below.VariableSampleSample standardVariabledescriptionmeandeviationhigh school SAT scorex = 1495.716802Sx = 109.915203yfreshman year GPAy = 3.260911Sy0.492802r = 0.481202slope = 0.002157Determine the y-intercept, a, of the least-squares regression line for this data. Give your answer precise to at least fourdecimal places.a =

Given: r = 0.481202 slope = 0.002157 Now, Using the formula a=Y-slope×X Where Y = 3.260911 Slope =…

Answered: Determine the y-intercept, a, of the…

Determine the y-intercept, a, of the least-squares regression line for this data. Give your answer precise to at least four decimal places. a =

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

Related questions

Q: The given paired data lists the heights (in inches) of various males who were measured on their…

A: Given that ; X Y X \cdot YX⋅Y X^2X2 Y^2Y2 52 69 3588 2704 4761 50 66 3300 2500 4356…

Q: raised and spent (both in millions of dollars) by all congressional campaigns for 8 recent 2-year…

A: Given that:The table contains data related to the money raised and spent (both in millions of…

Q: Find the regression equation, letting the first variable be the predictor (x) variable. Find the…

A: Given : Internet users per 100(x) Nobel Laureates(y) 79.5 5.6 79.7 24.4 78.3 8.7 45 0.1…

Q: Make a scatter plot of the data and determine which type of model best fits the data. linear…

A: We would plot the points in a graph to determine the best fit model.

Q: The money raised and spent (both in millions of dollars) by all congressional campaigns for 8 recent…

A: Correlation is a statistical technique that is used to determine the association between the…

Q: Find the intercept (b0) for the regression equation for the following values. Round to 3 decimal…

Q: Refer to the data set: Part a: Make a scatterplot and determine which type of model best fits the…

A: If the data lies on a straight line, or seems to lie approximately along a straight line, a linear…

Q: Use the model to predict the amount of money spent by a customer who spends 11 minutes at the store.…

A: The regression equation is Dollar Spent=4.75+3.23*Time spent When time spent is 11 minutes then…

Q: The money raised and spent (both in millions of dollars) by all congressional campaigns for 8 recent…

A: The question is about regression.Given :Regression equation :To find :se and it's interpretation.

Q: Develop the estimated regression equation. What is the value of the y-intercept? Round to three…

A: Given information: X Y XY X^2 Y^2 105 173 18165 11025 29929 125 188 23500 15625 35344 135…

Q: find the intercept (b0) for the regression equation for the following values. Round to 3 decimal…

A: Given that X Y X \cdot YX⋅Y X^2X2 Y^2Y2 33 180 5940 1089 32400 25 170 4250 625 28900…

Q: 1. State your regression model (least-squares line). y=360.3622x + 4839.606 2. Use your model to…

Q: : Use the linear regression formulas to find the slope (a1) and the intercept (?0) of the best fit…

A: Given information:Data points:y-3.3-7.1-9.8-12.3-14-21.4-21.3-28.6-2To find:The slope of the…

Q: Develop the estimated regression equation. What is the value of the slope? (Round to three…

A: Solution: Given information: n= 30 ∑x=10400∑y=11463∑x2=4316874∑y2=4999521∑xy=4516851

Q: I attached the question

A: Step 1: Generating the regression equation: We have to find the estimated regression line, Where x…

Q: Refer to the data set: (1, 2.5), (2.5, 15), (0.5, 2), (-2, 0.5), (0, 1), (1.5, 5) Part a: Make a…

A: Scatter plot The linear regression model is best fit

Q: The following table compares the length of a rhinoceros horn (in inches) to its body length (in…

A: From given data, x Y X*X X*Y 34 111 3774 1156 37 114 4218 1369 40 124 4960 1600 43 134…

Q: An automotive engineer computed a least-squares regression line for predicting the gas mileage (y)…

A: Given : y = -0.14x + 38.78

Q: The following table compares the length of a rhinoceros horn (in inches) to its body length (in…

A: From given data, X Y X*Y X*X 35 111 3885 1225 38 121 4598 1444 41 132 5412 1681 44 133…

Q: Interpret the regression coefficient of X3 in relation to the Y ( X3 unit is mile) Y = 58.286 +…

A: The regression coefficient of X3 is given by 13.7604

Q: The data provided give the number of standby hours based on total staff present, X₁, and remote…

A: The given data is as follows: Standby HoursRemote HoursTotal Staff…

Q: Refer to the data set: Part a: Make a scatter plot and determine which type of model best fits the…

A: a) Use the excel spreadsheet to find the scatterplot for the given data. From the above figure it…

Q: data on retail price and energy cost for 10 large side-by-side refrigerators is reproduced in the…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: Find the equation of the regression line for the given data. Then construct a scatter plot of the…

A: Introduction: Consider that x is the independent variable and y is the dependent variable. The size…

Q: For a linear regression b1 is the estimated y-intercept, and b0 is the estimated slope of the…

A: The general form of linear regression equation is, y=b0+b1x

Q: What is the slope and intercept for the regression equation given this data? X = -5, 34, 56, 0, 61 Y…

A: The given paired observations for the variables X and Y are as follows:XY-513346356460-236150The…

Q: you take a bar of soap and weigh it after each shower. will the regression line be positive or…

A: Answer: Regression line be negative.

Q: Refer to the data set: (-1, 2), (1, 3), (1, 5), (2, 7), (3, 8), (4, 11) Part a: Make a scatter plot…

Q: The file Galton on D2L contains the 928 observations Francis Galton used in 1885 to estimate the…

A: Note: Hey there! Thank you for the question. As you have posted multiple sub-parts, we have solved…

Q: Find the least-squares regression line treating square footage as the explanatory variable. y =…

A: Table…

Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

Suppose a local university researcher wants to build a linear model that predicts the freshman year GPA of incoming students
based on high school SAT scores. The researcher randomly selects a sample of 40 sophomore students at the university and
gathers their freshman year GPA data and the high school SAT score reported on each of their college applications. He
produces a scatterplot with SAT scores on the horizontal axis and GPA on the vertical axis. The data has a linear correlation
coefficient of 0.481202. Additional sample statistics are summarized in the table below.
Variable
Sample
Sample standard
Variable
description
mean
deviation
high school SAT score
x = 1495.716802
Sx = 109.915203
y
freshman year GPA
y = 3.260911
Sy
0.492802
r = 0.481202
slope = 0.002157
Determine the y-intercept, a, of the least-squares regression line for this data. Give your answer precise to at least four
decimal places.
a =

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Correlation, Regression, and Association$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

Show your work please.
The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 63 inches. Is the result close to the actual weight of 442 pounds? Use a significance level of 0.05. Chest size (inches) 58 50 65 59 59 48 Weight (pounds) 414 312 499 450 456 260 Click the icon to view the critical values of the Pearson correlation coefficient r. What is the regression equation? Critical Values of the Pearson Correlation Coefficient r y=D+x (Round to one decimal place as ne Critical Values of the Pearson Correlation Coefficient r NOTE: To test Ho: p=0 against H,: p+0, reject Ho if the absolute value of r is greater than the critical value in the table. a = 0.05 a = 0.01 4 0.950 0.990 0.878 0.811 0.754 5 0.959 6 0.917 7 0.875 8 0.707 0.834 0.666 0.798 10 0.632 0.765 11 0.602 0.735 12 0.576 0.708 13 0.553 0.684 14 0.532 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482…
The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 40 inches. Is the result close to the actual weight of 352 pounds? Use a significance level of 0.05. Chest size (inches) *Weight (pounds) 44 54 328 528 41 55 39 51 418 580 296 503 Click the icon to view the critical values of the Pearson correlation coefficient r. - What is the regression equation? x (Round to one decimal place as needed.)
The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 57 inches. Is the result close to the actual weight of 476 pounds? Use a significance level of 0.05. 44 Chest size (inches) Weight (pounds) 58 48 51 58 60 425 266 347 453 282 408 Click the icon to view the critical values of the Pearson correlation coefficient r. ..... What is the regression equation? y=+x (Round to one decimal place as needed.) Activate Windows View an example Get more help- Help me solve this O Type here to search hp delete insert prt sc f12 f1o fg 1 f7 f6 f5 f3 米 IOI f1 esc hom backspace 6. L. 4 U E R tab F G J. A caps lock pause 00 9, %24 3. %23
Provide an example of a research project in your hometown where you would choose to use linear regression. What variable would be your Y-score, and what variable would be your X-score? What does a regression line represent? What is the standard error of estimate?
The data provided give the number of standby hours based on total staff present, X₁, and remote hours, X₂. Perform a multiple regression analysis using the data provided and determine the VIF for each independent variable in the model. Is there reason to suspect the existence of collinearity? Click the icon to view the data. Determine the VIF for each independent variable in the model. | VIF ₂2 = VIF₁ = (Round to three decimal places as needed.) Is there reason to suspect the existence of collinearity? OA. No. The VIF for each independent variable is less than 5. B. Yes. The VIF for each independent variable is greater than 5. OC. No. The VIF for each independent variable is greater than 5. OD. Yes. The VIF for each independent variable is less than 5. wwwwwww Table of Data Standby Total Staff Hours Present 245 330 274 358 195 197 117 153 115 275 200 236 336 339 321 303 286 329 352 323 Remote Hours 417 655 524 385 349 350 388 153 278 479 Print Done
The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c Click the icon to view the monthly data. a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costs = 247733.3 +(43.2000) x Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, bo. if appropriate. Choose the correct answer below. OA. The value of by is the predicted overhead costs for 0 billable hours. OB. For each increase of 1 unit in overhead costs, the predicted billable hours are estimated to increase by bo OC. It is not appropriate to interpret by. because its value is the predicted…
The table shows the average weekly wages (in dollars) for state government employees and federal government employees for 8 years. The equation of the regression line is y = 1.493x - 83.403. Complete parts (a) and (b) below. A Average Weekly Wages (state), x Average Weekly Wages (federal), y 764 1003 766 1048 791 1119 (a) Find the coefficient of determination and interpret the result. r² = 0 (Round to three decimal places as needed.) 800 1152 843 1201 887 1250 924 1277 939 1306
Is it reasonable to interpret the y-intercept of the regression line? Why or why not? One home that is 1,750 square feet is listed at $590,000. Is this home's price above or below average for a home of this size? Use residuals and show your work to answer. footaget) ## (Intercept) 21.14411 136.31449 0.155 0.87954 ## footage 0.28388 0.08516 3.333 0.00667 ** ## Residual standard error: 71.64 on 11 degrees of freedom ## Multiple R-squared: 0.5025, Adjusted R-squared: 0.4573 ## F-statistic: 11.11 on 1 and 11 DF, p-value: 0.006671
Compute the least-squares regression equation for the given data set. Round the slope and yFintercept to at least four decimal places. 4 y 7. 3. Send data to Excel Regression line equation: y =|