Regression methods were used to analyze thedata from a study investigating the relationshipbetween roadway surface temperature (x) andpavement deflection (v). Summary quantitieswere2020202020Σx 1478 , Σy- 12.75, Σ x-1432 15.8 , Σ.-8.86 and Σ xy 1083.67n=1n=1n=1n=1n=1 f. What proportion of variation in thepavement deflection is explained by thevariation in the surface temperature?g. Test for significance of regression using a= 0.05.1. What is the teststatistics.2. What is the criticalvalue.3. What conclusions canyou draw?4. Find the p-value for thistest.h. Estimate the standard errors of the slope.i. Estimate the standard errors of theintercept.

Given Information : Regression method are used to analyze the data from a study investigating the…

Regression methods were used to analyze the data from a study investigating the relationship between roadway surface temperature (x) and pavement deflection (v). Summary quantities were 20 20 20 20 20 Σx-1478 , Σν-12.75, Σx-1432 15.8, Σ,- 8.86 and Σ xy 1083.67 n=1 n=1 n=1 n=1 n=1

Regression methods were used to analyze the data from a study investigating the relationship between roadway surface temperature (x) and pavement deflection (v). Summary quantities were 20 20 20 20 20 Σx-1478 , Σν-12.75, Σx-1432 15.8, Σ,- 8.86 and Σ xy 1083.67 n=1 n=1 n=1 n=1 n=1

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

See similar textbooks

Related questions

Q: A research department of an American automobile company wants to develop a model to predict gasoline…

A: a) The regression equation is Y= 58.15708 -0.11753 Horsepower -0.00687 Weight Unit increase in…

Q: The random variables with the same mean the two regression equations are y= ax +b and x= ay + B, b…

Q: Consider the following linear regression model: (i) Derive the normal equations using OLS method.…

A: Linear Regression Model:yi=β0+β1x1i+β2x2i+β3x3i+uiui =yi-β0-β1x1i-β2x2i-β3x3iTo derive the normal…

Q: Consider the regression Y = a, + az X + a; Z+u. we know that if there is a strong linear correlation…

A: Given statement, 'if there is a strong linear correlation between X and Z then it is more likely…

Q: It is necessary to relate the per cent gas absorbed in a tower, Y, to the gas temperature X, and the…

A: Given, Percent gas absorbed in a tower Y to the gas temperature X1 and the vapor pressure of the…

Q: We wish to estimate the effect of weight on serum cholesterol (S. C.) level in healthy females aged…

A: Simple linear regression model: A simple linear regression model is given as y^ = b0 + bx + e…

Q: Some states permit only licensed firms to sell funeral goods (for example, caskets, urns) to the…

A: Given information: y^=1419+790·x1-254x2+263x1·x2 (71) (135) (105)R2=0.79

Q: 4.1 part d

A: (d)The sample standard deviation of the test scores across the 100 classrooms is,

Q: The results for the regression are as follows Coefficients Standard Error T stat…

A: Hi there! Thank you for posting the question. As you have posted multiple questions, as per the…

Q: The commercial division of a real estate firm is conducting a regression analysis of the…

A: Dear students as per guidelines we answer the first three subparts only. Please post other subparts…

Q: & Obtain the regression equations from the data given below: 1 2 9 8 3 4. 6. 8 10 12 11 13 14 16 15…

A: Solution is given:

Q: An engineer performed an experiment to determine the effect of CO2 pres- sure, CO, temperature,…

Q: The accompanying Minitab regression output is based on data that appeared in the article…

A: Given information: The MINITAB output for multiple linear regression is given.

Q: The first step of the Durbin-Watson test for the presence of autocorrelation is to estimate the…

A: Durbin-Watson test is used to detect autocorrelation between residual of regression analysis. The…

Q: A student used multiple regression analysis to study how family spending (y) is influenced by income…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: A study was recently performed by an agency in which it attempted to develop a regression model to…

A: a) Here, the variable x1 denotes the vehicle weight.

Q: A student used multiple regression analysis to study how family spending (y) is influenced by income…

A: The percentage of variation explained in the response variable by the independent variables is…

Q: emperature in Celsius (x) 10 20 30 40 50 60 70 80 90 Life time in Hours (y) 420 365 285 220 176 117…

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

Q: A particular article presented data on y = tar content (grains/100 ft3) of a gas stream as a…

A: The regression model is Mean y value=86.5-0.124x1+5.07x2-0.0708x3+0.001x4. In the model x3=x22 and…

Q: A multiple regression model has the form y^=b0+b1x1+b2x2 The coefficient b1 is interpreted as…

A: The coefficient b1 is interpreted as the:

Q: A student used multiple regression analysis to study how family spending (y) is influenced by income…

A: Hi, thanks for posting the question. Since there are more than three sub parts posted in the…

Q: A random sample of 102 observations is selected to estimate the relationship between the price of a…

A: The amount of percent variability of the used car values (dependent variable) explained by the model…

Q: In a linear regression aialysis of 60 observations, the two lines of regression are 100 Y = 768 X-…

Q: The owner of a mobile ice-crane believes that hot weather affects his sales. To investigate the…

A: Since you have posted a question with multiple sub parts, according to our guidelines we can solve…

Q: Q2. Why do we have in general, two lines of regression? Obtain the regression of Y on X and X on Y…

Q: A researcher has decided to estimate the following equation using an OLS regression. Y- bo + b; X, +…

A: The conditions required to perform OLS method in regression are linear relationship between…

Q: Following table shows the data of traffic density and accident ratio taken from Lahore Islamabad…

A: From the provided information, a) The regression equation can be obtained using excel steps as…

Q: A linear regression model has been estimated for the variables Y="monthly consumption of veal (kg)",…

A: The provided information is Y=monthly consumption of veal (kg) X1=monthly monetary household income…

Q: itere is a bivariate data set. Find the regression equation for the response variable y. 55.2 8.1…

A: Solution: The regression equation is obtained by using excel. Procedure: Enter the data in excel.…

Q: A student used multiple regression analysis to study how family spending (y) is influenced by income…

A: c. From the given information, The dependent variable is: family spending(y) The independent…

Q: The regression output from a model for predicting the heart weight (in g) of cats from their body…

A: (a) The null and alternative hypothesis is, The level of significance is, The sample size is, n =…

Q: You are asked to do quality control and quality assurance during the determination of lead…

A: Given Information: The linear regression equation is, y=1.97x+1.50 R2=0.99 and Standard deviation…

Q: A sample consists of 500 houses sold in Karachi between January 2020 and December 2020. The multiple…

A: As we can wee in the output, the value of R square is 0.67, which shows that the data is not a good…

Q: Regression methods were used to analyze the data from a study investigating the relationship between…

Q: The accompanying table shows partial regression results. ΑNOVA df SS MS F Significance F Regression…

A: Hypothesis : H0 : β1 = 0 , The variable X is not significantly related to variable Y H1 : β1 ≠ 0 ,…

Q: A student used multiple regression analysis to study how family spending (y) is influenced by…

A: The estimated regression equation is: y^ = a + b1X1 + b2X2 + b3X3 y^ = 0.0136 + 0.7992 X1 + 0.2280…

Q: Here is a bivariate data set. Find the regression equation for the response variable y. y 53.1 67.6…

A: Given observation and calculation x y x2 y2 xy 53.1 67.6 2819.61 4569.76…

Q: Þata on the relationship between plant age and dry matter in the stalk are given in the Table. X…

A: Given data represents plant age and dry matter in the stalk . The following data are passed :…

Q: The table below shows the average weekly wages (in dollars) for state government employees and…

A: Given: x y 717 1022 779 1053 785 1102 804 1153 855 1193 896 1245 923 1268 926…

Q: The ages, t years of 7 hospital patients and their blood pressure, p mmHg are shown in Table 3.…

A: Hi! Thank you for posting the question. Since your question has more than three sub-parts, we have…

Q: A microcomputer manufacturer has developed a regression model relating his sales (y=$10,000s) with…

A: Solution: Part 1: In this part, the sample size used for this analysis needs to be found. In the…

Q: Q4. The Omantel firm has estimate the Sales of fibre internet connections in Oman with the related…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Data on the relationship between plant age and dry matter in the stalk are given in the Table. X…

Q: 8. In an investigation to empirically determine the value of 1, a student measures the circumference…

A: We want to predict the value of the circumference from the diameter of the circle, and based on this…

Q: 3. A study of beer consumption using the annual data from 1980 -2001 produced the following…

A: Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you…

Q: In an experiment to measure the stiffness of a spring, the length of the spring under different…

A: To measure the stiffness of spring, length of the spring under different loads as measured as…

Q: An engineer at a semiconductor company wants to model the relationship between the device HFE (y)…

A: Formula : MSR = SSR/df_Regression

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

Regression methods were used to analyze the
data from a study investigating the relationship
between roadway surface temperature (x) and
pavement deflection (v). Summary quantities
were
20
20
20
20
20
Σx 1478 , Σy- 12.75, Σ x-1432 15.8 , Σ.-8.86 and Σ xy 1083.67
n=1
n=1
n=1
n=1
n=1

f. What proportion of variation in the
pavement deflection is explained by the
variation in the surface temperature?
g. Test for significance of regression using a
= 0.05.
1. What is the test
statistics.
2. What is the critical
value.
3. What conclusions can
you draw?
4. Find the p-value for this
test.
h. Estimate the standard errors of the slope.
i. Estimate the standard errors of the
intercept.

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 with 5 images

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

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
Given the table below, Let y, x1, x2, and x3 be the time of concentration (t, in hr), watershed length (L in ft), watershed slope (S in %), and runoff curve number (CN): Evaluate the linear multiple regression model with two or three predictor variables. Compute the multiple correlation coefficient, the standard error of estimate, and the standard deviation of the variable y. Discuss the reliability of the model
You are asked to do quality control and quality assurance during the determination of lead concentration in a city’s tap water using ICP-AES. Plotting ICP -AES signal as a function of lead concentration (in ppb) gave you a linear regression equation of y = 1.97x + 1.50 with an R^2=0.99. The instrumental response (signal) had a standard deviation of 0.75. What is the limit of quantitation in terms of lead concentration (ppb) of this instrumental method?
Following table shows the data of traffic density and accident ratio taken fromLahore Islamabad Motorway in the first quarter of 2018.Traffic Density X 30 35 40 45 50 60 70 80 90Accident Ratio Y 2 4 5 5 8 15 24 30 32a. Determine the equation for the estimated regression line of Y on Xb. Calculate the coefficient of determination.c. Find the product moment coefficient of correlation
A sample consists of 500 houses sold in Karachi between January 2020 and December 2020. The multiple linear regression analysis is carried out to predict the house prices for investment in residential properties in Karachi, Pakistan. The output below is produced using SPSS. Model Unstandardized Coefficients t VIF Constant 14.208 5.736 Age of house -0.299 -2.322 1.58 Square footage of the house 0.364 2.931 1.71 Income of families in the area 0.004 0.392 1.01 Transportation time to major markets -0.337 -2.619 1.90, R2 = 0.67; DW = 2.08 How would you interpret the above ‘Output’ of a regression analysis performed in SPSS?
A researcher at a large company has collected data on the beginning salary and current salary of 50 randomly selected employees. The correlation between the data sets is r = 0.912. The summary statistics from the data collected are shown bellow: Beginning Salary Ending Salary Mean x¯=56,340 y¯=82,070 Standard deviation Sx = 5,470 Sy = 7,800 Use a complete sentence to describe the strength and direction of the linear relationship between beginning salary and current salary. Find the equation of the least-squares regression line. (Round to two decimal places)
Here is a bivariate data set. Find the regression equation for the response variable y. x y -18.8 -22.2 0 -48.4 7.9 -4.6 26.2 52.8 50.5 87.9 35.9 45.4 24.4 13.2 55.1 93.7 Regression Equation: Enter the equation in slope-intercept form (y=mx+b)(y=mx+b) with parameters accurate to three decimal places.
The least-squares regression equation is y=647.8x+17,858 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7507. predict the median income of a region in which 20% of adults 25 years and older have at least a bachelor's degree. Round to the nearest dollar as needed.
A multiple regression model has the form y^=b0+b1x1+b2x2 The coefficient b1 is interpreted as the:A. change in y per unit change in x1, holding x2 constantB. change in the average value of y per unit change in x1, holding x2 constantC. change in y per unit change in x1, when x1 and x2 values are correlatedD. change in y per unit change in x1 If multicollinearity exists among the independent variables included in a multiple regression model, the:A. multiple coefficient of determination will assume a value close to zeroB. standard errors of the regression coefficients for the correlated independent variables will increaseC. regression coefficients will be difficult to interpretD. regression coefficients will be difficult to interpret and the standard errors of the regression coefficients for the correlated independent variables will increase please explain which answer is correct and why
The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millions) are shown in the table. Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 569.The equation of the regression line is y=32.409x+17,285.501. Issues, x 410 467 679 499 497 394 62 53 189 174 Proceeds, y 18,223 28,066 43,757 31,337 35,488 35,312 22,180 10,660 30,384 28,416 Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 569. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest million dollars as needed. Type your answer in standard form where "3.12 million" means 3,120,000.) A. There is a 95% chance that the predicted proceeds given 569 issues is between $____ and $____. B. We can be 95% confident…
A microcomputer manufacturer has developed a regression model relating his sales (y=$10,000s) with three independent variables. The three independent variables are price per unit(Price in $100s), advertising( ADV in $1000s) and the number of product lines (Lines). Part of the regression results is shown below. Coefficient Standard Error Intercept 1.0211 22.8752 Price(X1) -0.1524 0.1411 ADV (X2) 0.8849 0.2886 Lines(X3) -0.1463 1.5340 Source d.f. S.S. Regression 3 2708.61 Error 14 2840.51 Total 17 5549.12 What has been the sample size (n) for this analysis? Use the above results to find the estimated multiple…
Disk drives last time Here is a scatterplot of the residu-als from the regression of the hard drive prices on their sizes from Exercise 18.a) Are any assumptions or conditions violated? If so,which ones?b) What would you recommend about this regression?