Given are five observations for two variables, x and y . What does the scatter d

Question

Given are five observations for two variables, x and y.

What does the scatter diagram indicate about the relationship between the two variables?
SelectThere appears to be a linear relationship between x and yThere appears to be a nonlinear relationship between x and yItem 2  

Develop the estimated regression equation by computing the the slope and the y intercept of the estimated regression line (to 1 decimal).
=   +  x

Use the estimated regression equation to predict the value of y when x = 3 (to 1 decimal).
=  

xi 1 2 3 4 5 yi 4 6 6 10 15

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: yi
Independent Variable: xi
yi = 0.4 + 2.6 xi
Sample size: 5
R (correlation coefficient) = 0.93819419
R-sq = 0.88020833
Estimate of error standard deviation: 1.7511901

Parameter estimates:

Analysis of variance table for regression model:

Hence,

Scatter Diagram 2 is correct.

There appears to be a linear relationship between x and y

Regression equation: y = 0.4 + 2.6 x

For x = 3, y = 0.4 + 2.6(3) = 8.2

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 0.4 1.8366636 0 3 0.2177862 0.8416 Slope 2.6 0.55377492 0 3 4.6950483 0.0183

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