Question

(Typed work preferable. Show step-by-step please! Answer fully.)

I used SPSS to create a bivariate regression equation where “MaleLifeExp” is the dependent variable and “Literacy” is the independent variable. The variable “Literacy” measures the percentage of people in each country who are able to read.

Model Summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.680 a	0.463	0.458	6.592

a. Predictors: (Constant), Literacy: Percentage of Adults Who Can Read Coefficients ^a

Model		Understated Coefficients B	Understated Coefficients Std. Error	Standardized Coefficients Beta	t	Sig.
(Constant)		39.784	2.897		13.735	0.000
Literacy: Percentage of Adults Who Can Read		.324	.034	.680	9.648	0.000

a. Dependent Variable: MaleLifeExp: Male Life Expectancy at Birth

A) Interpret both key components of the regression equation.

B) Is the slope coefficient in the regression equation statistically significant (that is, using an alpha level of .05, can we reject a null hypothesis of no association)? Be sure to explain what information you use to determine whether the component is statistically significant or not.

C) Use the results of your regression results to predict the average male life expectancy in a country in which only 25% of the population can read. Compare this predicted value to the average male life expectancy in a country in which 85% of the population can read.

Answer 1

We have given output of the bivariate regression model from thr SPSS output.

Here y is dependent variable is MaleLifeExp and x is independent variable is Literacy

A). Here bo = intercept is equal to 39.784 and

b1 is slope coefficient is 0.324 here both are positive if x value increases Yhat value increases

Yhat = bo + b1*x. Estimate equation

B) check coefficient is significant or not

To test Ho: B1 =0 vs H1: B1 not equal to zero

Test statistic t= (b1- B1) / SE b1

t = (0.324 - 0)/0.034 = 9.648

P value = 0

Decision : we reject Ho if p value is less than alpha value

Here p value is less than alpha value we reject Ho

Conclusion : here coefficient of the slope is significant

C) predict value when x value 25%

Yhat = 39.784 + (0.324*25) = 47. 884

And predict value when x is equal to 85%

Yhat = 39.774 (0.324*85). = 67.324

When x value increases prediction value increases because here constant and slope coefficient is positive here prediction value is greater than for x is 85 %. Than x is equal to 25%.