Scm 415 Hw 1

Logan Means

SCM 415

HW 1

Expenditure

[pic 1]

1. Looking at the plot, it suggests that there is a linear relationship between Y(expenditure) versus x(income).
2. Call:

lm(formula = expenditure ~ income)

Residuals:

     Min           1Q               Median             3Q               Max

-1598.63     -216.35         -53.47            395.80         873.49

Coefficients:

                    Estimate Std.    Error            t value         Pr(>|t|)    

(Intercept) 135.16267        371.54130   0.364           0.719    

income        1.23358           0.06006       20.540        <2e-16 ***

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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 526.9 on 29 degrees of freedom

Multiple R-squared:  0.9357,        Adjusted R-squared:  0.9335

F-statistic: 421.9 on 1 and 29 DF,  p-value: < 2.2e-16

From the R output, we can see that β0 and β1 are 135.16267 and 1.23358, and the estimate of σ is 526.9.

1. From the R output, we can see the standard error of the estimated value of β1 = 0.06006. Since this is a very small number, the estimation is far more accurate. Looking at the P-value, it is <2.2e-16. Since that number is way smaller than 2.5% we can reject the null hypothesis.
2.                       2.5 %                97.5 %

(Intercept)  -624.72461      895.04995

income          1.11075          1.35641

From this R Output, we can see that a 95% confidence interval for 0 is (-624.72461, 895.04995) and a 95% confidence interval for 1 is (1.11075, 1.35641). [pic 2][pic 3]

1. From the R Output, we can see that the Multiple R-Square value is 0.9357. Since this number is pretty close to 1, we can conclude that the data fits the model and that most of the variation of Y can be explained by X.

Electricity [pic 4]

1. Looking at the plot, it suggests there is a linear relationship between Y(hourly electricity power consumption during the peak period) versus X(monthly electricity power consumption).
2. Call:

lm(formula = Y ~ X)

Residuals:

    Min         1Q               Median            3Q              Max

-4.1399     -0.8275        -0.1934         1.2376         3.1522

Coefficients:

                      Estimate Std.          Error             t value             Pr(>|t|)   

(Intercept)   -0.8313037          0.4416121      -1.882             0.0655 .  

X                     0.0036828          0.0003339      11.030           4.11e-15 ***

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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1