Question

The annual sales of American made vehicles (in 1000 vehicles) to foreign countries has been estimated as follow:

E(Y_i)=200.5 - 4.5X₁ + 1.8X_2i - 3.76X₃   R²=0.73

  (1.081)^* (-2.73)^* (3.932)^{* (}-5.03)^*    n=44, F=18.56

Where E(Y_i)= annual average number of vehicles sold to foreign countries (in 1000 vehicles), X₁=the annual average price of all vehicles sold to foreign countries (in $100), X₂= average foreign per capita income (in $1000), and X_{3 is a binary variable that assumes a value of 0 when there is no major political turmoil in foreign countries in a year, and a value of 1 when there is a major turmoil in foreign countries in a year.}

^*Numbers inside parentheses are t-statistics.

a. Explain the meaning of each estimated coefficient (except the intercept) in the context of this problem and plain English.

b. Use alpha of 0.05 to determine which estimated coefficients are significant (different from zero) including the intercept. Make sure all null hypotheses and alternative hypotheses are explained in the context of this model and plain English. Also, find the approximate P-values. What are your conclusions?

c. Check the overall significance (or validity) of the entire model using alpha=0.05. Make sure H_o,H_a, and your conclusion are explained in plain English. What is the approximate p-value?

d. Explain the meaning of multiple coefficient of determination in the context of this model.

Please show work

Answer 1

E(Yi)=200.5 - 4.5X1 + 1.8X2i - 3.76X3

where

E(Yi)= annual average number of vehicles sold to foreign countries (in 1000 vehicles)

X1=the annual average price of all vehicles sold to foreign countries (in $100),

X2= average foreign per capita income (in $1000), and

X3 is a binary variable that assumes a value of 0 when there is no major political turmoil in foreign countries in a year, and a value of 1 when there is a major turmoil in oreign countries in a year.

a)

interpritation

if the value of X1=the annual average price of all vehicles sold to foreign countries (in $100), i incresed by 1 then value of annual average number of vehicles sold to foreign countries (in 1000 vehicles) is decreased by 4.5

if the value of X2= average foreign per capita income (in $1000) is ncresed by 1 then value of annual average number of vehicles sold to foreign countries (in 1000 vehicles) is increased by 1.8

if the value of X3 is a binary variable that assumes a value of 0 when there is no major political turmoil in foreign countries in a year, and a value of 1 when there is a major turmoil in oreign countries in a year. is ncresed by 1 then value of annual average number of vehicles sold to foreign countries (in 1000 vehicles) is decreased by 3.76

b. Use alpha of 0.05 to determine which estimated coefficients are significant (different from zero) including the intercept. Make sure all null hypotheses and alternative hypotheses are explained in the context of this model and plain English. Also, find the approximate P-values. What are your conclusions

first intercept is denoted as bo

the hypothsis

H0:b0=0 vs H1:b0≠0

test statisric value is t=1.081

the p value is 0.2862

the p value is grater than 0.05

so we accept H0 b0=0

i.e the intercept is insinificant for the model

first slpoe t is denoted as b1

the hypothsis

H0:b1=0 vs H1:b1≠0

test statisric value is t=-2.73

the p value is 0.0094

the p value is less than 0.05

so we reject H0 i.e b1≠0

i.e the x1 is sinificant for the model

nnual average price of all vehicles sold to foreign countries (in $100), is sinificant for the model

second slpoe is denoted as b2

the hypothsis

H0:b2=0 vs H1:b2≠0

test statisric value is t=-3.932

the p value is 0.0003

the p value is less than 0.05

so we reject H0 i.e b2≠0

i.e the x2 is sinificant for the model

average foreign per capita income (in $1000), is sinificant for the model

Third slpoe is denoted as b3

the hypothsis

H0:b3 =0 vs H1:b3≠0

test statisric value is t=--5.03

the p value is  0.0001

the p value is less than 0.05

so we reject H0 i.e b3≠0

i.e the x3  is sinificant for the model

is a binary variable that assumes a value of 0 when there is no major political turmoil in foreign countries in a year, and a value of 1 when there is a major turmoil in oreign countries in a year. is sinificant for the model

c. Check the overall significance (or validity) of the entire model using alpha=0.05. Make sure Ho,Ha, and your conclusion are explained in plain English. What is the approximate p-value?

the hpothesis is

H0:b1=b2=b3=0

H1: at least one bi is different from zero i=1,2,3

Test statistic value is  

F=18.56

the p value is 0.0001

the p value is less than 0.05

so we reject H0

at lest one bi is different

the all independent variable is significant for thr model;

d)

Explain the meaning of multiple coefficient of determination

coefficient of determination=R2=0.73

the 73% variation in y is explained by the independent variables