Question

Fitting a linear model using R a. Read the Toluca.txt dataset into R (this dataset can be found on Canvas). Now fit a simple linear regression model with X = lotSize and Y = workHrs. Summarize the output from the model: the least square estimators, their standard errors, and corresponding p-values. b. Draw the scatterplot of Y versus X and add the least squares line to the scatterplot. c. Obtain the fitted values ˆyi and residuals ei . Print the first 5 fitted values and the corresponding residuals.

lotSize workHrs

80 399

30 121

50 221

90 376

70 361

60 224

120 546

80 352

100 353

50 157

40 160

70 252

90 389

20 113

110 435

100 420

30 212

50 268

90 377

110 421

30 273

90 468

40 244

80 342

70 323

Answer 1

Given data

Toluca
x	y
80	399
30	121
50	221
90	376
70	361
60	224
120	546
80	352
100	353
50	157
40	160
70	252
90	389
20	113
110	435
100	420
30	212
50	268
90	377
110	421
30	273
90	468
40	244
80	342
70	323

Answer(a): the least square estimators, their standard errors, and corresponding p-values

Coefficients:
	Estimate	Std.	Error	t	value Pr(>|t|)
(Intercept)	62.366	26.177	2.382	0.0259	*
x	3.57	0.347	10.29	4.45E-10	***

Answer(b): scatterplot of Y versus X and the least squares line to the scatterplot

Answer(C): First five fitted values y_i and residuals e_i

y	y fitted	errors
399	347.982	51.01798
121	169.4719	-48.4719
221	240.876	-19.876
376	383.684	-7.68404
361	312.28	48.72