Problem 9b: To get the regression output for the hypothesis test: Stats Regressi

Question

Problem 9b: To get the regression output for the hypothesis test:

Stats Regression Regression Fit Regression Model input the same x and y OK

Regression Analysis: LWT versus BWT

Analysis of Variance

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

Regression       1    6068 6068.1     6.69    0.010

BWT            1    6068 6068.1     6.69    0.010

Error          187 169730   907.6

Lack-of-Fit 131 133641 1020.2     1.58    0.027

Pure Error    56   36090   644.5

Total          188 175799

Model Summary

      S   R-sq R-sq(adj) R-sq(pred)

30.1272 3.45%      2.94%       1.39%

Coefficients

Term         Coef SE Coef T-Value P-Value   VIF

Constant   106.87     9.14    11.69    0.000

BWT       0.00779 0.00301     2.59    0.010 1.00

Regression Equation

LWT = 106.87 + 0.00779 BWT

Fits and Diagnostics for Unusual Observations

Obs     LWT     Fit   Resid Std Resid

23 202.00 128.97   73.03       2.43 R

39 215.00 130.29   84.71       2.82 R

68 250.00 132.61 117.39       3.91 R

76 229.00 133.38   95.62       3.19 R

93 235.00 135.15   99.85       3.33 R

106 241.00 136.40 104.60       3.49 R

129 116.00 142.66 -26.66      -0.90     X

130 123.00 145.75 -22.75      -0.77     X

131 120.00 112.39    7.61       0.26     X

132 130.00 114.82   15.18       0.51     X

133 187.00 115.71   71.29       2.41 R X

147 200.00 121.89   78.11       2.61 R

171 187.00 125.31   61.69       2.06 R

183 190.00 126.08   63.92       2.13 R

R Large residual

X Unusual X

Include: What must you assume to analyze this data?

Explanation / Answer

Answer:

For the regression analysis of the given data, we must assume the following assumptions:

1] Normality: We will assume the two related populations follow an approximate normal distribution.

2] Linear relationship: For the regression analysis, data should be bivariate and there should be a significant relationship exists between the given two variables. For the given regression analysis, we get p-value as 0.00 which indicate significant relationship between the given two variables.

3] There would not be any existence of multicollinearity and auto-correlation for the given regression model. For the given regression model, the VIF is given as 1.00 which indicate that the predictors are not correlated with each other.

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