Question

Reserve Problems Chapter 11 Section 2 Problem 2 The peanut crop was harvested from five fields of various area. The following data are the mass of the crop from each field y (in kilograms) and the field area x (in hectares). y|7110 | 15600 13490 19960 | 13070 X 1.96 4.09 3.35 4.50 2.52 Round your intermediate answers to four decimal places (e.g. 98.7654). (a) Fit the simple linear regression model using the method of least squares. Find the estimate of 62. Round your answer to the nearest integer (e.g. 9876). = (b) What change in the mean mass is expected when the field area changes by 1 hectare? Round your answer to the nearest integer (e.g. 9876). BI (c) Calculate the fitted value of y corresponding to x = 3.35. Find the corresponding residual. Round your answer to the nearest integer (e.g. 9876). Round your answer to the nearest integer (e.g. 9876). e = (d) Estimate the mean mass of the crop harvested from 2.0 hectares. Round your answer to the nearest integer (e.g. 9876).

Answer 1

Solution

we will solve it by using excel and the steps are

Enter the Data into excel

Click on Data tab

Click on Data Analysis

Select Regression

Select input Y Range as Range of dependent variable.

Select Input X Range as Range of independent variable

click on labels if your selecting data with labels

click on ok.

So this is the output of Regression in Excel.

SUMMARY OUTPUT
Regression Statistics
Multiple R	1
R Square	1
Adjusted R Square	1
Standard Error	1944
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	75227439	75227439	20	0
Residual	3	11332681	3777560
Total	4	86560120
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	373	3142	0	1	-9626	10371	-9626	10371
x	4103	919	4	0	1177	7028	1177	7028

1. $\hat{\sigma }^{2}$ = MS Residual = 3777560

2. $\hat{\beta _{1}}$ = 4103

3. From above regression output we have the regression equation

y-hat = 373+4103*x

now predict y-hat when x = 3.35

y-hat = 373+4103*3.35

y-hat =14118

residual e = y - y-hat

e = 13490 - 14118

e = -628

d)

now predict y-hat when x = 2

y-hat = 373+4103*x

y-hat = 373+4103*2

y-hat =8579