Consider the following t table consising of 20 observations of the variable y an

Question

Consider the following t table consising of 20 observations of the variable y and time t 11.866 1258 11 1948 16 18.19 2 1063 7 12.68 12 1825 17 16 02 3 1166 8 13.08 13 1623 18 14 36 4 1351 9 12.58 14 16 84 19 17.30 5 1403 10 16.4015 17.01 20 17.71 a Inear rend model and a quadratic tend model (Negative values should be indicated by a minus sign Round your answers to 4 docimal places ear TrendQuadraic Intercept NA b 2. Which trend model descibes the data wel? Lnear trend modal based on the R measure Linear trend model based on the adjusted RF measure Quadratic trend model based on the R measure Quadratic trend model based on the adusted R measune

Explanation / Answer

The statistical software outputs for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: t
y = 11.481105 + 0.33703759 t
Sample size: 20
R (correlation coefficient) = 0.76275944
R-sq = 0.58180196
Estimate of error standard deviation: 1.736826

Parameter estimates:

Analysis of variance table for regression model:

Polynomial Regression Results:
Dependent Variable: y
Independent Variable: t
y = 9.7556667 + 0.80761176 X + -0.022408293 X^2

Parameter estimates

Analysis of variance table for polynomial regression model:

Summary of fit:
Root MSE: 1.6356819
R-squared: 0.6497
R-squared (adjusted): 0.6085

Hence,

b - 1) The table will be:

b - 2) Option D is correct.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 11.481105 0.80681033 0 18 14.230241 <0.0001 Slope 0.33703759 0.067351225 0 18 5.0041791 <0.0001

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