Interpret b3 in this estimated regression equation.b3 = 3.1 is an estimate of the change in y corresponding to a 1 unit change in X3 when X₁, X21and X4b3= -2.5 is an estimate of the change in y corresponding to a 1 unit change in X1 whenX2, X31constant.хаb3:= -2.7 is an estimate of the change in y corresponding to a 1 unit change inconstant.хаb4 = 3.1 is an estimate of the change in y corresponding to a 1 unit change inconstant.Interpret b4 in this estimated regression equation.b4 = -2.5 is an estimate of the change in y corresponding to a 1 unit change in x2constant.(b) PredictwhenX1, X3,b3 = 7.8 is an estimate of the change in y corresponding to a 1 unit change in x2b3 = 7.8 is an estimate of the change in y corresponding to a 1 unit change in x3 when X₁, X₂,andy whenX1Xwhen=10, X₂ = 5, x3 = 1, and x4 2.=X1'X21whenwhen X₁, X3,andX11 X21andandX4 are heldX3 are heldX4are held constant.X4and xb4and= 2.7 is an estimate of the change in y corresponding to a 1 unit change in x3 when X₁, X2,X₂ when X₁,X4b4= 7.8 is an estimate of the change in y corresponding to a 1 unit change inX31and x3 are held constant.4= 2.7 is an estimate of the change in y corresponding to a 1 unit change in x4 when X₁, X₂, and x3 are held constant.are held constant.are held constant.and X4 are heldX3 are heldare held constant. In a regression analysis involving 30 observations, the following estimated regression equation was obtained.ŷ = 17.9 + 3.1x₁ - 2.5x₂ + 7.8x3 + 2.7x4(a) Interpret b₁ in this estimated regression equation.1b₁ = 2.7 is an estimate of the change in y corresponding to a 1 unit change in x4 when X₁, X₂, and x3 are held constant.b₁ = 7.8 is an estimate of the change in y corresponding to a 1 unit change in X3 when X₁, X2, and x4 are heldconstant.b₁1=3.1 is an estimate of the change in y corresponding to a 1 unit change inwhenX1x2whenb₁ = 3.1 is an estimate of the change in y corresponding to a 1 unit change inb₁ = -2.5 is an estimate of the change in y corresponding to a 1 unit change inconstant.and X4X2, X31X1, X31X31andX4 are held constant.and x4 are heldX21X₁ whenb₂= 2.7 is an estimate of the change in y corresponding to a 1 unit change in X4constant.Interpret b₂ in this estimated regression equation.b2= 3.1 is an estimate of the change in y corresponding to a 1 unit change in X1 when X2, X3, and x4 are held constant.when X₁, X2andx2whenare held constant.x3X1, X31are heldb₂= -2.5 is an estimate of the change in y corresponding to a 1 unit change inconstant.b₂ == 7.8 is an estimate of the change in y corresponding to a 1 unit change in x3 when X₁, X2, and x4 are held constant.2² and x4 are heldb₂ = -2.5 is an estimate of the change in y corresponding to a 1 unit change in x₁ when X₂, X3,constant.and X4are held

Here: Given regression equation is y^=17.9+3.1X1-2.5X2+7.8X3+2.7X4 We have to interpret b1,b2,b3,b4…

Answered: (b) Predict y when x₁ = 10, X₂ = 5, X3…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
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?
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 16.7 + 3.5x1 − 2.3x2 + 7.9x3 + 2.9x4 (a)Interpret b1 in this estimated regression equation. -b1 = 7.9 is an estimate of the change in y corresponding to a 1 unit change in x3 when x1, x2, and x4 are held constant. -b1 = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x4 when x1, x2, and x3 are held constant. -b1 = 3.5 is an estimate of the change in y corresponding to a 1 unit change in x1 when x2, x3, and x4 are held constant. -b1 = 3.5 is an estimate of the change in y corresponding to a 1 unit change in x2 when x1, x3, and x4 are held constant. -b1 = −2.3 is an estimate of the change in y corresponding to a 1 unit change in x1 when x2, x3, and x4 are held constant.Interpret b2 in this estimated regression equation. -b2 = −2.3 is an estimate of the change in y corresponding to a 1 unit change in x1 when x2, x3, and x4 are held…
An investigation into the relationship between an adolescent mother's age x in years and the birth weight y of her baby in grams yielded the regression equation y= - 1163.45 + 245.15x as well as r = .88369, r2= .78091, SSE = 337212.45, and s= 205.30844 1) What is the predicted birth weight for a baby brn to a 17 year old woman? 2) What is the propotion of the variability in the weights of babies born to adolescent mothers that is accounted for by the mother's age? 3) For every additional year in the mother's age that mean birth weight of the baby? (a) increases by about 245g (b) decreases by about 245g (c) increases by about 1163g (d) increases by about 1163g (e) changes by an amount that cannot be determined from the information given.
The estimated regression equation for a model involving two independent variables and 10 observations follows. Y=25.7067 + 0.2795x1 + 0.7337x2 A. Interpret b1 and b2 in this estimated trgression equation. B1 = ? B2 = ? Thank you
Run a regression analysis on the following data set, where yy is the final grade in a math class and xx is the average number of hours the student spent working on math each week. hours/weekx Gradey 5 61 5 54 6 47.4 7 54.8 8 62.2 9 59.6 11 75.4 11 70.4 15 89 18 100 State the regression equation y=m⋅x+by=m⋅x+b, with constants accurate to two decimal places. What is the predicted value for the final grade when a student spends an average of 14 hours each week on math?Grade = Round to 1 decimal place.
Run a regression analysis on the following data set, where yyis the final grade in a math class and xxis the average number of hours the student spent working on math each week. hours/weekxGradey445.6548661.4107710771284.81376.21699.41910020100 State the regression equation y=m⋅x+by=m⋅x+b, with constants accurate to two decimal places. What is the predicted value for the final grade when a student spends an average of 15 hours each week on math? Grade = Round to 1 decimal place.
Run a regression analysis on the following data set, where yy is the final grade in a math class and xx is the average number of hours the student spent working on math each week. hours/weekx Gradey 4 51.6 5 43 13 82.2 14 90.6 15 89 16 80.4 16 89.4 18 97.2 19 91.6 19 97.6 State the regression equation with constants accurate to 2 decimal places.ˆyy^ = x + What is the predicted value for the final grade when a student spends an average of 11 hours each week on math? Round to 2 decimal places.
Shown below is a portion of a computer output for a linear regression analysis relating an individual's income (y in thousands of dollars) to age (x1 in years), level of education (x2 ranging from 1 to 5), and the individual's gender (x3 where 0 = female and 1 = male). Coefficient Standard Error t-statistic p-value Intercept 15.934 1.389 11.47 0.000 x1 0.625 0.094 6.65 0.000 x2 0.921 0.190 4.85 0.000 x3 –0.510 0.920 –0.55 0.590 Source of Variation Sum of squares Degrees of freedom Mean square F-statistic p-value Regression 84 3 28 4 0.027 Error 112 16 7 Total 196 19 a. Is there a significant relationship between an individual's income and the set of variables, age, level of education, and gender (based on a significance level α =05 )? Explain why using one of the p-values in the output tables. b.Which of the three predictor variables are…
Consider the following regression equation representing the linear relationship between the Canada Child Benefit provided for a married couple with 3 children under the age of 6, based on their annual family net income: ŷ =121.09−0.57246xR2=0.894 where y = annual Canada Child Benefit paid (in $100s) x = net annual family income (in $1000s) Source: Canada Revenue Agency a. As the net annual family income increases, does the Canada Child Benefit paid increase or decrease? Based on this, is the correlation between the two variables positive or negative?The Canada Child Benefit paid .The correlation between the two variables is .b. Calculate the correlation coefficient and determine if the relationship between the two variables is strong, moderate or weak.r= , the relationship is . Round to 3 decimal places c. Interpret the value of the slope as it relates to this relationship. For every $1 increase in annual family net income, there is a $0.57246 decrease in…
Consider the following regression equation representing the linear relationship between the Canada Child Benefit provided for a married couple with 3 children under the age of 6, based on their annual family net income: ŷ =121.09−0.57246xR2=0.894 where y= annual Canada Child Benefit paid (in $100s) x = net annual family income (in $1000s) Source: Canada Revenue Agency a. As the net annual family income increases, does the Canada Child Benefit paid increase or decrease? Based on this, is the correlation between the two variables positive or negative?The Canada Child Benefit paid ? .The correlation between the two variables is ? .b. Calculate the correlation coefficient and determine if the relationship between the two variables is strong, moderate or weak.r= , the relationship is ? . Round to 3 decimal places c. Interpret the value of the slope as it relates to this relationship. For every $1 increase in annual family net income, there is a $0.57246 decrease in…

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(b) Predict y when x₁ = 10, X₂ = 5, X3 = 1, and x4 = 2. X