C. Use Excel to develop a multiple linear regression model and use hypothesis te

ID: 3310711 • Letter: C

Question

C. Use Excel to develop a multiple linear regression model and use hypothesis testing to determine which regressors are significant. What should the numerical value of B3_hat be? Express your answer as an integer.

Problem 1. lhe electric power consumed each month by a chem- ical plant is thought to be rclated to the average ambient tem perature (x), the number of days in the month (r2), the average product purity (x), and the tons of product produced (). The past year's historical data are available and are presented in the following table: 24 21 24 100 95 110 25 31 45 60 65 72 80 84 75 60 50 38 240 236 290 274 301 87 91 94- 87 86 94 300 296 267 276 288 261 26 25 25 24 25 25 23 97 96 110 105 100 98 91 89

Explanation / Answer

Solution:

First of all we have to find multiple regression model by using excel which is given as below:

Regression Statistics

Multiple R

0.862988866

R Square

0.744749783

Adjusted R Square

0.598892516

Standard Error

15.57933272

Observations

ANOVA

Significance F

Regression

4957.240744

1239.310186

5.10601768

0.030302769

Residual

1699.009256

242.7156081

Total

6656.25

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-102.7132364

207.8588509

-0.49414897

0.636328637

-594.221316

388.7948432

0.605370537

0.368896954

1.641028833

0.144796622

-0.266932145

1.47767322

8.923644198

5.300522238

1.683540564

0.136145668

-3.61009923

21.45738763

1.437456733

2.391620508

0.601038806

0.566759239

-4.217827118

7.092740585

0.013609308

0.733821444

0.018545803

0.985720985

-1.721602674

1.748821289

Answer:

For the above regression model, the p-values for the given four regressors are greater than 5% level of significance or alpha value 0.05, so all regressors or independent variables are not statistically significant.

Now, we have to test for 3.

H0: 3 = 0 versus Ha: 3 0

3_hat = 1.437456733

Test statistic = t = 3_hat / SE(3_hat) = 1.437456733/2.391620508 = 0.601038806

P-value = 0.566759239

= 0.05

P-value > = 0.05

We do not reject the null hypothesis that 3 is not statistically significant.

There is insufficient evidence to conclude that 3 is statistically significant.

D. Use Excel to develop a multiple linear regression model and use hypothesis testing to determine which regressors are significant. What should the numerical value of B4_hat be? Express your answer as an integer.