Question

Shown below is a portion of a computer output for a regression analysing relating Y(dependent variable) and X(independent variable)

ANOVA

df SS

Regression    1    115.064

Residual 13    82.936

Coefficient    Standard error

Intercept 15.532    1.457

X -1.106 0.761

Required :- A) Perform a t test using the p value approach and determine whether x and y are related Let alpha=0.5 . B) Using the p value approach, perform an F test and determine whether x and y are related. C) Compute the coefficient of determination and fully interpret its meaning. Be specific.

Answer 1

Hello,

We have given the following parameters,

ANOVA	df	SS
Regression	1	115.064
Residuals	13	82.936

	Coeffi	standarded error
intercept	15.532	1.457
x	-1.106	0.761

A) Perform a t test using the p value approach and determine whether x and y are related Let alpha=0.5 .

est statistic. The test statistic is a t statistic (t) defined by the following equation.

t = b₁ / SE

t=-1.106/0.761=-1.453,

p-value is calculated in excel as, =t.dist(10.66,13,false)

	Coeffi	standarded error	t	p_value
intercept	15.532	1.457	10.66026	4.70052E-08
x	-1.106	0.761	-1.45335	0.136417558

Here as we compare the p-value with the 0.05 for the x value, the p-value is insignificant so we can conclude that there is no relation ship between the x and y.

B) Using the p value approach, perform an F test and determine whether x and y are related.

Answer :

ANOVA	df	SS	MSS	F	p-value
Regression	1	115.064	115.064	18.03597955	0.000953
Residuals	13	82.936	6.379692

we have calcualted mss=ss/df , f=mss_reg/mss_residaul, and f in excel as =f.dist(f,1,13)

from the above table we can say that there is best fit between the x and y.

C) Compute the coefficient of determination and fully interpret its meaning. Be specific.

oefficient of Determination (R²)

The coefficient of determination is a measure of the amount of variability in the data accounted for by the regression model. As mentioned previously, the total variability of the data is measured by the total sum of squares, . The amount of this variability explained by the regression model is the regression sum of squares, . The coefficient of determination is the ratio of the regression sum of squares to the total sum of squares.

=82.93/115.064=0.72