18 ) Use the following linear regression equation to answer the questions. x1 = 1.8 +...

18 ) Use the following linear regression equation to answer the questions.

x₁ = 1.8 + 3.1x₂ – 7.6x₃ + 1.5x₄

(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 = 9, x₃ = 10, and x₄ = 5, what is the predicted value for x₁? (Use 1 decimal place.)

d) 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 = 9 data points were used to construct the given regression equation and that the standard error for the coefficient of x₂ is 0.335. Construct a 90% 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 ±

Expert Solution

orchestra answered 2 years ago

Use the following linear regression equation to answer the questions. x1 = 1.3 + 3.6x2 –...

Use the following linear regression equation to answer the questions. x1 = 1.3 + 3.6x2 – 8.3x3 + 2.0x4 (Use the following linear regression equation to answer the questions. x1 = 1.3 + 3.6x2 – 8.3x3 + 2.0x4 (a) Which variable is the response variable? x3x2 x1x4 Which variables are the explanatory variables? (Select all that apply.) x3x2x4x1 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant x2 coefficient x3 coefficient x4 coefficient (c)...

Use the following linear regression equation to answer the questions. x1 = 1.1 + 3.0x2 –...

Use the following linear regression equation to answer the questions. x1 = 1.1 + 3.0x2 – 8.4x3 + 2.3x4 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. x3 = −16.2 + 3.8x1 +...

Use the following linear regression equation to answer the questions. x3 = −16.2 + 3.8x1 + 9.6x4 − 1.2x7 (a) Which variable is the response variable? x7 x1 x3 x4 Which variables are the explanatory variables? (Select all that apply.) x4 x7 x1 x3 (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 = -1, and x7 = 1, what is...

Use the following linear regression equation to answer the questions. x3 = −18.2 + 4.4x1 +...

Use the following linear regression equation to answer the questions. x3 = −18.2 + 4.4x1 + 8.2x4 − 1.2x7 Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant x1 coefficient x4 coefficient x7 coefficient If x1 = 3, x4 = -9, and x7 = 6, what is the predicted value for x3? (Round your answer to one decimal place.) x3 = Suppose x1 and x7 were held at fixed but arbitrary values. If x4...

Use the following linear regression equation to answer the questions. x3 = ?16.6 + 3.7x1 +...

Use the following linear regression equation to answer the questions. x3 = ?16.6 + 3.7x1 + 8.6x4 ? 1.9x7 (a) Which variable is the response variable? x4 x1 x3 x7 Which variables are the explanatory variables? (Select all that apply.) x4 x7 x1 x3 (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 = 4, x4 = -4, and x7 =...

Use the following linear regression equation regarding airline tickets to answer the question. (The dataset collected...

Use the following linear regression equation regarding airline tickets to answer the question. (The dataset collected for Distance was from 500 miles to 5,687 miles) Note: that Distance is the number of miles between the departure and arrival cities, and Price is the cost in dollars of an airline ticket. (a) Find the slope using the linear regression equation given to you above. Inter- pret the value that you got for the slope in the context of the problem. Predicted...

Linear regression equation

Linear regression equation also find accuracy Obtain regression equation of Y on X and estimate Y when X=55 from the following

Curve Fitting and Linear Regression a) Determine the linear regression equation for the measured values in...

Curve Fitting and Linear Regression a) Determine the linear regression equation for the measured values in the table above. ?? 1 2 3 4 Value 1 (????) 0 3 7 10 Value 2 (????) 2 4 9 11 b) Plot the points and the linear regression curve. c) Determine the Linear Correlation Coefficient (i.e., Pearson’s r) for the dataset in the table above.

9) Use the following data to estimate a linear regression equation between y and x. Interpret...

9) Use the following data to estimate a linear regression equation between y and x. Interpret the estimated slope coefficient. Predict y for an x value of 9. Calculate and interpret the model’s R-squared. x y 21 12 17 10 11 8 3 5 13 15

Run a linear regression using Excel’s Data Analysis regression tool. Construct the linear regression equation and...

Run a linear regression using Excel’s Data Analysis regression tool. Construct the linear regression equation and determine the predicted total sales value if the number of promotions is 6. Is there a significant relationship? Clearly explain your reasoning using the regression results. Number of Promotions Total Sales 3 2554 2 1746 11 2755 14 1935 15 2461 4 2727 5 2231 14 2791 12 2557 4 1897 2 2022 7 2673 11 2947 11 1573 14 2980

Question