Question

Problem: (parts a, b, & C-3 points each:-part d-16 points). This problem continues on the next pagg SUMMARYOUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0.913173122 0.83388515 0.832924949 13.03760503 175 CARSPENDtotal expenditure on new automobiles in the United States (s, billions) DISPOSINCnational disposable income in the United States (S, billions) ations ANOVA df MS Regression 1147618.0707 147618.0707 868.4481311 2.43543E-69 173 29406.39206 169.9791449 174 177024.4628 Coefficients Starndard Eror Stat Lower 95% Upper 95% 20.1767114 1.562143144 12.9160451 0129299790.000438759 29.46944402 2.43543E-69 3.73025Е-27 17.0933981 23.2600247 DISPOSINC 0.012063969 0.013795989 Dependent variable CARSPEND Independent variable DISPOSINC a) Write out the equation for this model b) Briefly comment on the goodness of fit for this model with respect to the data e) Interpret the DISPOSINC coefficient in this model d The DISPOSINC for 1975 through 1979 (in billions of dollars) are given below: 1975 $430.2999878 1976 1977 1978 1979 438.2999878 445.7000122 451.8999939 460.1000061 Predict CARSPEND for each of those years

Answer 1

Answer

(A) we know that regression equation is given as y = ax + b

where y is dependent variable, x is independent variable, a is slope and b is intercept

Using the data table given above, we can write the following equation

CARSPEND = 20.1767114 + 0.012929979*(DISPOSINC)

This is the required equation for this model.

(B) Goodness of fit is strong for model because the p value corresponding to the intercept and independent variable slope are less than 0.05 significance level, which means both values are significant enough. Similarly, the overall F statistics value is also significant which shows that there is a significant relationship between the dependent and independent variable.

(C) Disposinc coefficient for the given model is 0.012929979, which is a positive value. This means that for every 1 unit increase in the independent variable disposinc, there will be an increase of 0.012929979 unit in the Carspend or dependent variable.

(D) We have the regression equation

CARSPEND = 20.1767114 + 0.012929979*(DISPOSINC)

For 1975, we have to put disposinc = 430.2999878

we get,

CARSPEND = 20.1767114 + 0.012929979*(430.2999878) = 25.7404812

For 1976, we have to put disposinc = 438.2999878

we get,

CARSPEND = 20.1767114 + 0.012929979*(438.2999878) = 25.8439210

For 1977, we have to put disposinc = 445.7000122

we get,

CARSPEND = 20.1767114 + 0.012929979*(445.7000122) = 25.9396032

For 1978, we have to put disposinc = 451.8999939

we get,

CARSPEND = 20.1767114 + 0.012929979*( 451.8999939) = 25.0197688

For 1979, we have to put disposinc = 460.1000061

we get,

CARSPEND = 20.1767114 + 0.012929979*(460.1000061) = 26.1257948