Consider the following table, consisting of 20 observations of the variable y an

Question

Consider the following table, consisting of 20 observations of the variable y and time t. 1 9.50 6 13.05 11 16.43 16 15.27 2 12.94 715.19 12 15.15 17 17.53 3 13.40 8 6.25 13 14.36 18 14.94 4 14.45 913.29 14 17.49 19 18.32 5 14.73 10 14.26 15 18.75 20 17.67 b-1. Estimate a linear trend model and a quadratic trend model. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.) Linear Trend Variable Quadratic Trend Intercept NA Adjusted R2 b-2. Which trend model describes the data well? Linear trend model based on the R measure Linear trend model based on the adjusted R2 measure Quadratic trend model based on the R2 measure Quadratic trend model based on the adjusted R2 measure

Explanation / Answer

The statistical software outputs for linear and quadratic trends are:

Simple linear regression results:
Dependent Variable: y
Independent Variable: t
y = 12.136895 + 0.28681955 t
Sample size: 20
R (correlation coefficient) = 0.76602674
R-sq = 0.58679697
Estimate of error standard deviation: 1.4629219

Parameter estimates:

Polynomial Regression Results:
Dependent Variable: y
Independent Variable: t
y = 11.246149 + 0.52975017 X + -0.011568125 X^2

Parameter estimates

Summary of fit:
Root MSE: 1.4587093
R-squared: 0.612
R-squared (adjusted): 0.5663

Hence,

b - 2) Option B is correct.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 12.136895 0.67957324 0 18 17.859583 <0.0001 Slope 0.28681955 0.056729678 0 18 5.0558995 <0.0001

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---