Use the following linear regression equation to answer the questions.
x1 = 1.4 + 3.7x2 – 8.3x3 + 1.8x4
(c) If x2 = 2, x3 = 6,
and x4 = 10, what is the predicted value for
x1? (Use 1 decimal place.)
Suppose x3 and x4 were
held at fixed but arbitrary values and x2
increased by 1 unit. What would be the corresponding change in
x1?
Suppose x2 increased by 2 units. What would be
the expected change in x1?
Suppose x2 decreased by 4 units. What would be
the expected change in x1?
(e) Suppose that n = 16 data points were used to construct
the given regression equation and that the standard error for the
coefficient of x2 is 0.384. Construct a 99%
confidence interval for the coefficient of x2.
(Use 2 decimal places.)
lower limit | |
upper limit |
(f) Using the information of part (e) and level of significance 1%,
test the claim that the coefficient of x2 is
different from zero. (Use 2 decimal places.)
t | |
t critical ± |
c)
predicted value for x1 =1.4+3.7*2-8.3*6+1.8*10=-23
for x2 increased by 1 unit; corresponding change in x1 =3.7
for x2 increased by 2 unit; corresponding change in x1 =7.4
for x2 increased by 4 unit; corresponding change in x1 =14.8
e)
for 99% CI ; critical t=3.055
lower limit =estimate -t*std error =3.7-0.384*3.055=2.53
upper limit=estimate +t*std error =3.7+0.384*3.055=4.87
f)
t=estimate/std error =3.7/0.384=9.64
tcitical =-/+ 3.055 ~3.05
Use the following linear regression equation to answer the questions. x1 = 1.4 + 3.7x2 –...
Use the following linear regression equation to answer the questions. x1 = 1.4 + 3.1x2 – 8.2x3 + 2.1x4 Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1? Suppose x2 increased by 2 units. What would be the expected change in x1? Suppose x2 decreased by 4 units. What would be the expected change in x1? (e) Suppose that n = 13 data points...
Use the following linear regression equation to answer the questions. X1 = 1.7 + 3.6x2 - 8.4x3 + 1.5x4 (a) Which variable is the response variable? O X1 O X2 O X4 O X3 Which variables are the explanatory variables? (Select all that apply.) X3 X1 U X2 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X2 coefficient X3 coefficient X4 coefficient (c) If x2 = 8, X3 = 5, and x4...
Use the following linear regression equation to answer the questions. x3 = −16.5 + 4.5x1 + 8.4x4 − 1.5x7 (a) Which variable is the response variable? x4x3 x7x1 Which variables are the explanatory variables? (Select all that apply.) x4x7x3x1 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant x1 coefficient x4 coefficient x7 coefficient (c) If x1 = 3, x4 = -10, and x7 = 8, what is the predicted value for x3? (Round...
Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.4x2 – 8.3x3 + 2.3x4 (a) Which variable is the response variable? Which variables are the explanatory variables? (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant? x2 coefficient? x3 coefficient? x4 coefficient? (c) If x2 = 1, x3 = 8, and x4 = 6, what is the predicted value for x1? (Use 1 decimal place.) (d) Explain how...
Use the following linear regression equation to answer the questions. x1 = 1.7 + 3.9x2 - 8.1X3 + 1.9x4 (a) Which variable is the response variable? O O O O Which variables are the explanatory variables? (Select all that apply.) o X3 O X4 Сх, (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X2 coefficient Xz coefficient x4 coefficient (C) If x2 = 8, X3 = 3, and X4 = 1, what...
Consider the sample regression equation y-12+3x1-5x2+7x3-2x4 When x1 increases by 1 unit and x2 increases by 2 units, while x3 and x4 remain unchanged, what change would you expect in the predicted y Multiple Choice Decrease by 4 Decrease by 7 Decrease by 2 No change in predicted y
In a regression analysis involving 30 observations, the following estimated regression equation was obtained.A. Interpret b1, b2, b3, and b4 in this estimated regression equation. Assume that for each coefficient statement, the remaining three variables are heldconstant.b1 = estimated change in y per 1 unit change in x1b2 = estimated change in y per 1 unit change in x2b3 = estimated change in y per 1 unit change in x3b4 = estimated change in y per 1 unit change in...
All Greens is a franchise store that sells house plants and lawn and garden supplies. Although All Greens is a franchise, each store is owned and managed by private individuals. Some friends have asked you to go into business with them to open a new All Greens store in the suburbs of San Diego. The national franchise headquarters sent you the following information at your request. These data are about 27 All Greens stores in California. Each of the 27...
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. y=17.6+3.8x1-2.3x2+7.6x3+2.7x4 For this estimated regression equation SST= 1805 and SSR=1756. a. At a= 0.05 , test the significance of the relationship among the variables. SSE=_________________ (to 1 decimal, if necessary) MSR=________________ (to 1 decimal, if necessary) MSE=+_______________ (to 2 decimals, if necessary) What is the value of the F test statistic (to 1 decimal)? _______________ What is the p-value? - Select your answer -less than .01,between...
Answer the following question for where Y has been regressed on X1, X2, and X3. Use the linear regression output in the Excel file. Your answers should be rounded to 2 decimal places. a. What is the equation for the line of best fit or regression line? b. The proportion is for the amount of the variability of Y that is explained or accounted for by the model. C. The correlation between the observed values of y and the expected...