In the least-squares line y -5+ 3x, what is the marginal change in y for each unit change in x?
Q: The least squares error of a candidate measures how well that candidate line fits the data: E(m) =…
A: For least square method we need two things. 1. data points (xi, yi)2. fitting model, yi' = mxi + c…
Q: A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 319.32…
A: From the printout, the required values are obtained as follows: a = 319.32 b = -32.190 R-Sq = 97.8%…
Q: We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the…
A: The table shows the MINITAB regression output.-
Q: uppose the least squares regression line for predicting weight (in pounds) from height (in inches)…
A: Solution: The least squares regression line for predicting weight (in pounds) from height (in…
Q: 4b. Find the equation of the least squares line for the given data (-2,-1). (0.2). (1.3). (2.2).
A:
Q: A student at a junior college conducted a survey of 20 randomly selected full-time students to…
A:
Q: he annual number of retail drug prescriptions (in millions) can be approximated by the least…
A: x = 0 corresponds to the year 2018 It means, x = 10 corresponds to the year 2028 because 2028…
Q: In the least squares line y =6+7x, what is the marginal change in ŷ for each unit change in x? 07 13…
A: The least squares line is .
Q: We use the form = a + bx for the least-squares line. In some computer printouts, the least-squares…
A: Let y = a+bx be the regression line. Here a is the intercept (or) and b is the Slope coefficient…
Q: We use the form ý = a + bx for the least-squares line. In some computer printouts, the least-squares…
A: Solution According to guidelines we solve three subpart
Q: Find the best quadratic least squares fit to the data x 0 1 2 3 y 3 2 4 4
A:
Q: 9. The equation of the least-squares line for the number of three-base hits (triples) and the number…
A: The independent variable is the number of three-base hits. The dependent variable s the number of…
Q: We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the…
A: a) In this case, the predictor or the independent variable is “Elevation” and the dependent or…
Q: In the least-squares line ý = 5 + 6x, what is the marginal change in ý for each unit change in x?
A:
Q: A researcher found that the linear regression equation has a slope of 3 and an intercept of -6. What…
A: The objective of this question is to find the predicted value of Y for a given value of X using the…
Q: Your school is trying to refine its textbook budget. The following table shows the average cost of…
A: Solution-: Let, X=be the average cost of a textbook and Y=be the curriculum year Given data: X Y…
Q: Use five decimal places Fit the following data by the equation y=(a*x)/(b+x) using the Least…
A: Given: The given equation is y=axb+x x 2 4 10 13 y 15 32 40 24
Q: We use the form = a + bx for the least-squares line. In some computer printouts, the least-squares…
A: Solution
Q: Sandor is trying to identify a linear relationship linking the amount of heat (x) applied in the…
A: The given data is Heat (oF) Strength index 2400 820 1800 600 2000 840 1200 620 2600 920…
Q: You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale,…
A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…
Q: Find a least-squares best fit line for the points (1, 1), (2, 5), (3, 5). Write your answer as a…
A:
Q: . A study performed by a psychologist determined that a person's sense of humor is linearly related…
A: We have given that humor = -49 + 1.8(IQ) When individual IQ score of 110
Q: b. Find the least-squares curve of the form above to fit the data (5,1.54), (7,2.02), (9,2.5),…
A: The data is given by x y 5 1.54 7 2.02 9 2.5 11 2.8 13 3.2 15 3.5 17 3.8 19…
Q: what would the maximum return be?
A: for x = 10000 y = 60000
Q: Show that Var(Y − a − bX) ≤ Var(Y) where a and b are the intercept and the slope of the linear…
A:
Q: Sandor is trying to identify a linear relationship linking the amount of heat (x) applied in the…
A: Given The data is as follows: Heat (oF), x Strength index, y 2400 820 1800 600…
Q: An issue of USA Today reported the average fees charged to use another bank's ATM for 2000-2005.…
A: Basics:
Q: . The following data represents the projected global efense spending (in trillion of dollars) from…
A: 9) Given data points are, a) Excel Procedure: Enter t and defense spending in Excel>Data>Data…
Q: A scientist collected data on the mating call frequency of frogs and temperature. They found the…
A: Given data least square regression line : y^ = 3 + 5xhere x is temperature (in celsius) and y is…
Q: An issue of USA Today reported the average fees charged to use another bank's ATM for 2000-2005.…
A: The straight-line trend is given by, Y=a+bt,where, a is the intercept, b is the slope of the lineThe…
Q: Slatisties eourse has found sömething interesting: there may be a relationship between scores on his…
A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…
Q: Given the data points r1 = -1, x2 = 1, x3 = 2 and the correspond values, respectively, y1 = 1, y2 =…
A: We are given the data : x1=-1x2=1x3=2andy1=1y2=1y3=2 Forming a table , we have : x y xy x2 y2…
Q: A motorist found that the efficiency of her engine could be increased by adding lubricating oil to…
A: Let us denote X as the amount of lubricating oil and Y as the efficiency. Excel Procedure: Enter X…
Q: We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the…
A: Here, the independent variable is elevation (in thousands of feet) and the dependent variable is the…
Q: The average remaining lifetimes for women of various ages in a certain country are given in the…
A: Given : n=5 , ƩX=190 , ƩY=223.4, ƩX^2=11300 , ƩXY=4750 Our aim is to find the (a) equation of…
Q: The scatter plot below shows data for the average cost of a high-end computer (y, in dollars) in the…
A: Given Data Least square regression line The slope is 314x It tells that in each year, the average…
Q: We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares…
A: We have given that Elevation is listed under predictor. This means that elevation is the…
Q: Use partial derivatives to obtain the formula for the best least-squares fit to the data points.…
A:
Q: The annual expenditure for cell phones varies by the age of an individual. The average annual…
A: At what age is the yearly expenditure for cell phones the greatest .
Q: In the least-squares line = 5 – 9x, what is the value of the slope? When x changes by 1 unit, by…
A: In the least-squares line = 5 – 9x, what is the value of the slope?
![**Question 1: [-/1 Points]**
**DETAILS**
**BBUNDERSTAT11 9.2.002.**
In the least-squares line \( \hat{y} = 5 + 3x \), what is the marginal change in \( \hat{y} \) for each unit change in \( x \)?
[Submit Answer]
**Explanation:**
The question relates to understanding linear regression, specifically the interpretation of the slope in the least-squares regression equation. The equation given is \( \hat{y} = 5 + 3x \), where:
- \( \hat{y} \) is the predicted value of the dependent variable.
- \( 5 \) is the y-intercept, indicating the value of \( \hat{y} \) when \( x = 0 \).
- \( 3 \) is the slope of the line, representing the marginal change in \( \hat{y} \) for each unit change in \( x \). This means for every one unit increase in \( x \), \( \hat{y} \) increases by 3 units.
There are no graphs or diagrams in this image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5422827a-7860-4e7c-8a0f-f4498bf171e7%2F5c3f4e8f-d27f-4568-b784-2c2d4998180f%2Fzis5th_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
- We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 315.27 28.31 11.24 0.002 Elevation -31.812 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.8% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ = + x (b) For each 1000-foot increase in elevation,…We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 316.08 28.31 11.24 0.002 Elevation -31.974 3.511 -8.79 0.003 S = 11.8603 R-Sq = 97.8% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ = 316.08 +-31.974x For each 1000-foot increase in…We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 316.62 28.31 11.24 0.002 Elevation -30.516 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2% The printout gives the value of the coefficient of determination r2. What is the value of r? Be sure to give the correct sign for r based on the sign of b. (Round your answer to four decimal places.) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares…
- We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T. Constant 317.97 28.31 11.24 0.002 Elevation -28.572 3.511 -8.79 0.003 S = 11.8603 R-Sq 94.2% %3D Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (a) Use the printout to write the least-squares equation. %3D (b) For each 1000-foot increase in elevation, how many fewer frost-free days are…We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Сoef SE Coef T Constant 317.43 28.31 11.24 0.002 Elevation -31.272 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ = 317.43 -31.272 (b) For each 1000-foot increase in elevation, how many fewer…We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Сoef SE Coef T Constant 315.81 28.31 11.24 0.002 Elevation -31.650 3.511 -8.79 0.003 S = 11.8603 R-Sq = 94.6% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ : + %| (b) For each 1000-foot increase in elevation, how many fewer frost-free days…
- The residual plot shows the residuals for the least- squares line relating price of a used car (y) to the number of miles driven (x). Residuals Residual Plot for Miles Driven vs Price 10,000 5,000 -5,000 50,000 100,000 150,000 200,000 Number of Miles Driven Based on the residual plot, is the linear model appropriate for the relationship between miles and price? No, because there are clear outliers in the residual plot. No, because there is a clear curved pattern in the residual plot. No, because there does not appear to be a pattern to the residuals. Yes, because there is a clear curved pattern in the residual plot. Yes, because there does not appear to be a pattern to the residuals.We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from Climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in Colorado locations. A Minitab printout provides the following information. Predictor Constant Elevation Coef 315.00 -29.166 SE Coef 28.31 3.511 I 11.24 -8.79 P 0.002 0.003 S = 11.8603 R-Sq = 96.44 Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (c) The printout gives the value of the…An article gave data on a measure of pollution (in micrograms of particulate matter per cubic meter of air) and the cost of medical care per person over age 65 for six geographical regions of the United States. Find the equation of the least-squares line describing the relationship between y = medical cost and x = pollution. (Give the answer to two decimal places.) ŷ = Region North eBook Upper South Deep South West South Big Sky West Additional Materials Pollution Cost of Medical 30.0 922 31.8 898 32.1 975 26.8 979 30.4 959 40.0 906
- We use the form ý = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. %3D A Minitab printout provides the following information. Predictor Сoef SE Coef P Constant 315.54 28.31 11.24 0.002 Elevation -28.950 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (a) Use the printout to write the least-squares equation. = 315.54 X x (b) For each 1000-foot increase in elevation, how many fewer frost-free…Do not show any work on this question. For these ordered pairs: (0, 0.1), (1, 1), (2,2.4),(4,3.7), and (5, 5.7): Find (f ,y) and plot it as well as the five given points. Find the equation ofthe least squares regression line. Round off the x coefficient and the constant to the nearest onethousandth. Graph the equation together with the points above. If needed do not use a Pvalue to answer any problem. No credit will be given if a P value is used. Use only criticalvalues.A motorist found that the efficiency of her engine could be increased by adding lubricating oil to fuel. She experimented with different amounts of lubricating oil and the data are Amount of lubricating oil (ml) Efficiency (%) 0 25 50 75 100 | 60 70 75 81 84 (a) Obtain the least squares fit of a straight line to the amount of lubricating oil. (b) Test whether or not the slope B, = 0. Take a = 0.05 as your level of significance. (c) Construct a 90% confidence interval on the mean response at xo = 10 ml.
