1.Remind me if Xs are extremely correlated (scatterplot, VIF, Correlations) if you entertain a wonder switch, emend the seat by throwing one of the inconstants out of the copy. Consider R-squared or adj R-squared when making the resolution.

My Y = Revenue, my assemblage call is Amazon

X inconstants = Earnings, Revenue, and Assiduity Revenue.

As illusionn in the chief graph over, The X inconstants are wonderificant and illusion some direct copy thus-far it is not a mature direct continuity so we can say it is non-linear. The P- rates are cipher which instrument there is an attraction of a kinsman among the inconstants. X inconstants are so statistically wonderificant and co-related as the interkinsman matrix consultation illusions the equality of interkinsman among the inconstants. Merely Assiduity Fruits and Rights has a low interkinsman as it has 0.447.

Comparing my consultations I do see a wonder switch in the Employment as it has a privative wonder (-0.000573).

Interpreting the retrogression separation in my succor graph, we lack there to be a kinsman among our X and Y inconstant. X is the fractions inconstant and Y is our trusting inconstant. So, the kinsman among X and Y is if the X diversifys our Y diversifys as well-mannered. The constants are not statistically wonderificant as the P-values are important than 1. Let’s wear that the ace is 1, My coefficient in Rights is 114.5 that instrument is if my Rights extensions by $1, the Fruits conciliate extension by $114.5. In my succor X inconstant, if my Assiduity Fruits is extensiond by $1 then my Fruits so extensions by $370.1. Also, for the Employment it has a privative coefficient so that instrument they conciliate provoke on the irreconcilable course. Which instrument if the assemblage employs past than 1 idiosyncratic the fruits conciliate reduce by 0.000573. There is a very low impression so for the assemblage to see a enormous dissonance in the reduce of the fruits the assemblage conciliate deficiency to engage past than 10,000 employs which would reduce by$5.73.

WORKSHEET 1

**Regression Analysis: Fruits versus Earnings**

**Regression Equation**

Revenue | = | -67933 + 114.91 Earnings |

**Coefficients**

Term | Coef | SE Coef | T-Value | P-Value | VIF |

Constant | -67933 | 5923 | -11.47 | 0.000 | |

Earnings | 114.91 | 8.45 | 13.60 | 0.000 | 1.00 |

**Model Summary**

S | R-sq | R-sq(adj) | R-sq(pred) |

9225.39 | 67.27% | 66.91% | 65.08% |

**Analysis of Variance**

Source | DF | Adj SS | Adj MS | F-Value | P-Value |

Regression | 1 | 15742520392 | 15742520392 | 184.97 | 0.000 |

Earnings | 1 | 15742520392 | 15742520392 | 184.97 | 0.000 |

Error | 90 | 7659698627 | 85107763 | ||

Lack-of-Fit | 84 | 7637913547 | 90927542 | 25.04 | 0.000 |

Pure Error | 6 | 21785079 | 3630847 | ||

Total | 91 | 23402219018 |

**Fits and Diagnostics for Unusual Observations**

Obs | Revenue | Fit | Resid | Std Resid | |

88 | 60450 | 32387 | 28063 | 3.10 | R |

90 | 52890 | 34685 | 18205 | 2.02 | R |

91 | 56580 | 35145 | 21435 | 2.38 | R |

92 | 72380 | 35259 | 37121 | 4.12 | R |

*R Large residual*

**Durbin-Watson Statistic**

Durbin-Watson Statistic = | 0.186035 |

Considering the R-squared and the VIF consultation I entertain governmentd to capture my Employment and assiduity fruits out. There was a low R-squared in all my three X inconstants when I ran the Retrogression separation, so I governmentd to prefer the one delay the improve R-Square and R-sq(adj). The foremost R-sq is the Rights so I conciliate be maintenance merely one X inconstant. Also, The P-rate is O which is good-natured-natured and VIF is one which is low thus-far this is the best copy I entertain comparatively. So contemplateing at my VIF which is 1 there is no wonder of multicollinearity as it is not important than 5 or 10.

2. Using the plant concocts you generated, fulfill any nondirect kinsmans among Y and X inconstants.

Try to emend nonlinearity through intercharge (page 233-237). If it labors, haunt the transformed rendering of the inconstant. Otherwise, use the createer inconstant, propound the nonlinearity, and provoke on to the contiguous proof. Use 2 divergent intercharges (ex: Log X, 1/X, X^2 or SQRT(X)).

I ran a intercharge to see if my nonlinearity diversifys. Transforming a axioms instrument to diversify its professional create, so I ran Y and X inconstant to see if my Scatterconcoct afford me a direct or non-direct copy. Intercharge is one way to haunt the notification contented, but we diversify the professional create so it is not certain to regularly labor. However, I do not see complete diversifys. I ran Log X and SQRT (X) as my intercharge proof, but I got corresponding results. The chief graph is my Rights and the succor is intercharge delay Log X and third is SQRT (X). So, I entertain no precious to propound it and to provoke on delay my non-linearity.

3.Once you emend for nonlinearity and multicollinearity, restrain for autointerkinsman using DW proof. Do you entertain autocorrelation? Emend for autointerkinsman if you entertain any.

Based on my axioms since I entertain governmentd to haunt honorable one of my x inconstants that is Earnings. The DW = 0.186035 **Durbin-Watson Statistic**

Durbin-Watson Statistic = | 0.186035 |

In my 90 row I entertain inferior skip of 1.64 and the preferable skip 1.69. My DW is inferior than the inferior skip inveterate on my resolution government I am going to decline the trifling and I entertain an auto interrelation. So now I am attacking to fix the auto interkinsman so I conciliate entertain one past coefficient. I am going to add a lag rate of Yt to attack to invert showy it is future from the Yt.

So my row is 90 and K=1DL

WORKSHEET 1

**Regression Analysis: Fruits (yt) versus Earnings, Revenue(yt-1), incline**

**Method**

Rows unused | 1 |

**Regression Equation**

Revenue (yt) | = | -8952 + 16.4 Earnings + 1.0062 Revenue(yt-1) - 37 trend |

**Coefficients**

Term | Coef | SE Coef | T-Value | P-Value | VIF |

Constant | -8952 | 19638 | -0.46 | 0.650 | |

Earnings | 16.4 | 39.8 | 0.41 | 0.681 | 117.98 |

Revenue(yt-1) | 1.0062 | 0.0517 | 19.47 | 0.000 | 3.39 |

trend | -37 | 174 | -0.21 | 0.833 | 123.53 |

**Model Summary**

S | R-sq | R-sq(adj) | R-sq(pred) |

3933.62 | 94.21% | 94.01% | 93.00% |

**Analysis of Variance**

Source | DF | Adj SS | Adj MS | F-Value | P-Value |

Regression | 3 | 21921168164 | 7307056055 | 472.24 | 0.000 |

Earnings | 1 | 2638051 | 2638051 | 0.17 | 0.681 |

Revenue(yt-1) | 1 | 5864694800 | 5864694800 | 379.02 | 0.000 |

incline | 1 | 692178 | 692178 | 0.04 | 0.833 |

Error | 87 | 1346180110 | 15473335 | ||

Total | 90 | 23267348275 |

**Fits and Diagnostics for Unusual Observations**

Obs | Revenue (yt) | Fit | Resid | Std Resid | ||

77 | 22720 | 30943 | -8223 | -2.16 | R | |

80 | 35750 | 27150 | 8600 | 2.23 | R | |

81 | 29130 | 37634 | -8504 | -2.22 | R | |

84 | 43740 | 34958 | 8782 | 2.28 | R | |

85 | 35710 | 46101 | -10391 | -2.75 | R | |

88 | 60450 | 46171 | 14279 | 3.77 | R | |

89 | 51049 | 63046 | -11997 | -3.41 | R | X |

90 | 52890 | 53781 | -891 | -0.24 | X | |

91 | 56580 | 55662 | 918 | 0.25 | X | |

92 | 72380 | 59354 | 13026 | 3.64 | R | X |

*R Large residual X Unusual X*

**Durbin-Watson Statistic**

Durbin-Watson Statistic = | 2.46865 |

I ran the retrogression adding a lag, Incline and Revenue(yt-1) which gave me a improve VIF which is past than 117.98 in my X inconstant. It urban my DW which is 2.46865 which instrument there is no autointerkinsman detected in the scantling. However, I entertain detected Multicollinearity due to improve VIF. It illusions the multicollinearity among my X inconstant and incline. The T-rate from twain Rights and incline are not wonderificant as we can see the P-values which are over 0.05 for twain Rights and incline. This is a effect of multicollinearity among them two. If I decline the Incline the T-rate for rights conciliate be wonderificant. DW suppress to suppress to 0 indicates actual autointerkinsman and suppress to 4 indicates privative autocorrelation. When its suppress to 2 there is no autointerkinsman and that is accurately what we lack in the copy.

So repeatedly, I governmentd to reprovoke incline from my axioms and run the retrogression separation repeatedly. This gave me a mature copy which is illusionn in the graph beneath.

**Regression Analysis: Fruits (yt) versus Earnings, Revenue(yt-1)**

**Method**

Rows unused | 1 |

**Regression Equation**

Revenue (yt) | = | -4892 + 8.14 Earnings + 1.0037 Revenue(yt-1) |

**Coefficients**

Term | Coef | SE Coef | T-Value | P-Value | VIF |

Constant | -4892 | 4117 | -1.19 | 0.238 | |

Earnings | 8.14 | 6.54 | 1.24 | 0.216 | 3.21 |

Revenue(yt-1) | 1.0037 | 0.0500 | 20.07 | 0.000 | 3.21 |

**Model Summary**

S | R-sq | R-sq(adj) | R-sq(pred) |

3912.21 | 94.21% | 94.08% | 93.27% |

**Analysis of Variance**

Source | DF | Adj SS | Adj MS | F-Value | P-Value |

Regression | 2 | 21920475987 | 10960237993 | 716.10 | 0.000 |

Earnings | 1 | 23720949 | 23720949 | 1.55 | 0.216 |

Revenue(yt-1) | 1 | 6165533565 | 6165533565 | 402.83 | 0.000 |

Error | 88 | 1346872288 | 15305367 | ||

Total | 90 | 23267348275 |

**Fits and Diagnostics for Unusual Observations**

Obs | Revenue (yt) | Fit | Resid | Std Resid | ||

77 | 22720 | 31089 | -8369 | -2.17 | R | |

80 | 35750 | 27259 | 8491 | 2.20 | R | |

81 | 29130 | 37719 | -8589 | -2.25 | R | |

84 | 43740 | 34912 | 8828 | 2.30 | R | |

85 | 35710 | 46023 | -10313 | -2.73 | R | |

88 | 60450 | 46113 | 14337 | 3.80 | R | |

89 | 51049 | 62933 | -11884 | -3.36 | R | X |

90 | 52890 | 53611 | -721 | -0.19 | X | |

91 | 56580 | 55492 | 1088 | 0.30 | X | |

92 | 72380 | 59203 | 13177 | 3.63 | R | X |

*R Large residual X Unusual X*

**Durbin-Watson Statistic**

Durbin-Watson Statistic = | 2.46554 |

4.Incorporate seasonal dummies and incline into your copy. Fulfill if you entertain seasonality, incline by restraining their wonderificance? Is that accordant delay your prior findings?

Dummy inconstant are so determined the indicator inconstants it is how we cement non consecutive or imported end in our separation. So, incorporating incline and seasonality in our retrogression copy, Yt which is our trusting inconstant and is so a power of X1 which is Earnings. The coefficient in face of X1 is the conclusive goods and beta cipher is the arrest and untruths. Anything that is not explained in the copy that conciliate go to the untruth order. So, let us cement it in the copy so untruth can contemplate considerable improve. Incline is going to haunt a trace of the calculate of years. My scantling bigness is 92 so the incline conciliate extension in the increments of 1. Similarly, seasonality would be into lewd quarters Q1,Q2,Q3 and Q4.

WORKSHEET 1

**Regression Analysis: Fruits versus Earnings, T, q1, q2, q3**

**Method**

Categorical predictor coding | (1, 0) |

**Regression Equation**

q1 | q2 | q3 | |||

0 | 0 | 0 | Revenue | = | 27041 - 71.5 Earnings + 800 T |

0 | 0 | 1 | Revenue | = | 22892 - 71.5 Earnings + 800 T |

0 | 1 | 0 | Revenue | = | 22473 - 71.5 Earnings + 800 T |

0 | 1 | 1 | Revenue | = | 18324 - 71.5 Earnings + 800 T |

1 | 0 | 0 | Revenue | = | 22774 - 71.5 Earnings + 800 T |

1 | 0 | 1 | Revenue | = | 18625 - 71.5 Earnings + 800 T |

1 | 1 | 0 | Revenue | = | 18206 - 71.5 Earnings + 800 T |

1 | 1 | 1 | Revenue | = | 14057 - 71.5 Earnings + 800 T |

**Coefficients**

Term | Coef | SE Coef | T-Value | P-Value | VIF |

Constant | 27041 | 44784 | 0.60 | 0.548 | |

Earnings | -71.5 | 90.6 | -0.79 | 0.432 | 120.16 |

T | 800 | 388 | 2.06 | 0.042 | 120.14 |

q1 | |||||

1 | -4267 | 2664 | -1.60 | 0.113 | 1.50 |

q2 | |||||

1 | -4568 | 2662 | -1.72 | 0.090 | 1.50 |

q3 | |||||

1 | -4149 | 2661 | -1.56 | 0.123 | 1.50 |

**Model Summary**

S | R-sq | R-sq(adj) | R-sq(pred) |

9022.42 | 70.09% | 68.35% | 64.94% |

**Analysis of Variance**

Source | DF | Adj SS | Adj MS | F-Value | P-Value |

Regression | 5 | 16401476827 | 3280295365 | 40.30 | 0.000 |

Earnings | 1 | 50676370 | 50676370 | 0.62 | 0.432 |

T | 1 | 345468005 | 345468005 | 4.24 | 0.042 |

q1 | 1 | 208856960 | 208856960 | 2.57 | 0.113 |

q2 | 1 | 239764768 | 239764768 | 2.95 | 0.090 |

q3 | 1 | 197858706 | 197858706 | 2.43 | 0.123 |

Error | 86 | 7000742191 | 81403979 | ||

Total | 91 | 23402219018 |

**Fits and Diagnostics for Unusual Observations**

Obs | Revenue | Fit | Resid | Std Resid | |

88 | 60450 | 35030 | 25420 | 2.92 | R |

89 | 51049 | 31134 | 19915 | 2.30 | R |

90 | 52890 | 30632 | 22258 | 2.60 | R |

91 | 56580 | 31565 | 25015 | 2.92 | R |

92 | 72380 | 36443 | 35937 | 4.17 | R |

*R Large residual*

**Durbin-Watson Statistic**

Durbin-Watson Statistic = | 0.126943 |

5.Once you emended for all practicable problems, rewrite your conclusive equation, INTERPRET the equation, and prevent y, for 35th in scantling remark.

6.Analyze the resulting residuals (4-in-11 concoct in MINITAB)

7.How does retrogression separation percreate compared to univariate methods you entertain conversant? Create a consultation that includes the MSD for the univariate copys (Trend, Smoothing, Decomposition) and MSE of retrogression copy. (**HINT 1: You don’t entertain to try ALL univariate copys. Use your conversance of your axioms. For example: If your fruits inconstant is inclineing, no deficiency to run uncombined smoothing. Or, if it is direct, no deficiency to run nondirect incline copys etc. HINT 2:Your conclusive is about the nook, no mischief in reviewing the prior representative afore of term, either.)**

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