The agronomist believed that the amount of rainfall as well as the amount of fertilizer used would affect the crop yield. She did the experiment in the following way. Thirty greenhouses were rented. In each, the amount of fertilizer and the amount of water were varied. At the end of the growing season, the amount of corn was recorded. Use ?=0.05 a) Determine the sample regression line and interpret the coefficients b) Do these data allow us to infer that there is a linear relationship between the amount of fertilizer and the crop yield? c) Do these data allow us to infer that there is a linear relationship between the amount of water and the crop yield? d) What can you say about the fit of the multiple regression model? e) Is it reasonable to believe that the error variable is normally distributed with constant variance (Support your answer)? PLEASE ONLY USE EXCEL AND SHOW ALL EXCEL COMMANDS! Yield Fetilizer Water 201 100 1000 325 200 1000 124 300 1000 129 400 1000 344 500 1000 193 100 2000 369 200 2000 210 300 2000 306 400 2000 297 500 2000 339 100 3000 334 200 3000 273 300 3000 347 400 3000 331 500 3000 221 100 4000 396 200 4000 304 300 4000 381 400 4000 316 500 4000 286 100 5000 293 200 5000 355 300 5000 441 400 5000 321 500 5000 377 100 6000 392 200 6000 361 300 6000 432 400 6000 464 500 6000

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The agronomist believed that the amount of rainfall as well as the amount of fertilizer used would affect the crop yield. She did the experiment in the following way. Thirty greenhouses were rented. In each, the amount of fertilizer and the amount of water were varied. At the end of the growing season, the amount of corn was recorded. Use ?=0.05

a) Determine the sample regression line and interpret the coefficients

b) Do these data allow us to infer that there is a linear relationship between the amount of fertilizer and the crop yield?

c) Do these data allow us to infer that there is a linear relationship between the amount of water and the crop yield?

d) What can you say about the fit of the multiple regression model?

e) Is it reasonable to believe that the error variable is normally distributed with constant variance (Support your answer)?

PLEASE ONLY USE EXCEL AND SHOW ALL EXCEL COMMANDS!

Yield	Fetilizer	Water
201	100	1000
325	200	1000
124	300	1000
129	400	1000
344	500	1000
193	100	2000
369	200	2000
210	300	2000
306	400	2000
297	500	2000
339	100	3000
334	200	3000
273	300	3000
347	400	3000
331	500	3000
221	100	4000
396	200	4000
304	300	4000
381	400	4000
316	500	4000
286	100	5000
293	200	5000
355	300	5000
441	400	5000
321	500	5000
377	100	6000
392	200	6000
361	300	6000
432	400	6000
464	500	6000

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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