multiple regression

Multiple regressions and multiple correlations deals with the relationship of one variable

compared with a number of other variables. It is similar to the bivariate correlation

because it describes the degree of linear relationship between two variables. Though the

multiple correlation assigns one variable to be the criterion or dependent variable and

the other variable is the total of the independent variable or predictor. The total of the

independent variable is found by computing weights so the correlation between the

predictor and the criterion is as large as possible. The multiple regression is better

than the bivariate regression because it examines curvilinear relationships between

variables and investigates interactions between continuous independent variables.

In the present experiment the multiple regression and multiple correlation was used to

compare different predictors of reading skills. It was thought that working memory ability

was not as good of a predictor of reading skill as exposure to print. The results from

this experiment showed that the overall correlation was significant, (R = .59, F (5,147)

= 15.45, p * .0001) meaning adding one adding one variable to the prediction equation

significantly increases the degree of multiple correlation. It was also shown that the

best predictors for reading ability were exposure to print (t (142) = 5.501, p * .0001)

and non-verbal ability measured by the Raven’s test (t (142) = 2.953, p * .01). The

standardized regression equation for the significant coefficients was Z reading = .385Z

Multiple regressions and multiple correlations deals with the relationship of one variable

compared with a number of other variables. It is similar to the bivariate correlation

because it describes the degree of linear relationship between two variables. Though the

multiple correlation assigns one variable to be the criterion or dependent variable and

the other variable is the total of the independent variable or predictor. The total of the

independent variable is found by computing weights so the correlation between the

predictor and the criterion is as large as possible. The multiple regression is better

than the bivariate regression because it examines curvilinear relationships between

variables and investigates interactions between continuous independent variables.

In the present experiment the multiple regression and multiple correlation was used to

compare different predictors of reading skills. It was thought that working memory ability

was not as good of a predictor of reading skill as exposure to print. The results from

this experiment showed that the overall correlation was significant, (R = .59, F (5,147)

= 15.45, p * .0001) meaning adding one adding one variable to the prediction equation

significantly increases the degree of multiple correlation. It was also shown that the

best predictors for reading ability were exposure to print (t (142) = 5.501, p * .0001)

and non-verbal ability measured by the Raven’s test (t (142) = 2.953, p * .01). The

standardized regression equation for the significant coefficients was Z reading = .385Z

ART .224Z Ravens. The partial correlation, meaning the correlation between two variables

after variations from other variables were removed was .419 for exposure to print and .219

for non-verbal ability. The standardized regression equation for all the predictors was

Z reading= .119Z workmem .385Z ART .224Z Ravens .080Z GPA .150Z IQ.

Using a stepwise regression analysis it was found that the overall regression was

significant, (R = .574, F (5,147) = 23.623, p * .0001). The best predictors for reading

ability were exposure to print (t (142) = 5.884, p * .0001) non-verbal ability (t (142) =

3.279, p * .001) and IQ (t (142) = 2.181, p * .05) and the predictors had partial

correlations of, .440, .264 and .179, respectively. The regression equation in

standardized form for the stepwise regression analysis was Z reading = .408Z ART .248Z

Ravens .168ZIQ. The difference between the first standardized regression equation was

the stepwise regression only includes the variables that significantly contributed to the

prediction. Therefore, working memory and GPA were excluded in the stepwise regression

because they were not good predictors of reading ability. It was also shown that the

stepwise regression was a better type of regression because it was able to significantly

predict predictors (F (2, 140) = 2.278, ns).

For the curve estimates the regression coefficient was significant for the linear

component (t (1,146) = 6.150, p * .00001) therefore there was a positive linear

relationship between reading ability and exposure to print. The regression coefficients

were not significant for the quadratic component (t (1,146) = -.583, ns) or the cubic

after variations from other variables were removed was .419 for exposure to print and .219

for non-verbal ability. The standardized regression equation for all the predictors was

Z reading= .119Z workmem .385Z ART .224Z Ravens .080Z GPA .150Z IQ.

Using a stepwise regression analysis it was found that the overall regression was

significant, (R = .574, F (5,147) = 23.623, p * .0001). The best predictors for reading

ability were exposure to print (t (142) = 5.884, p * .0001) non-verbal ability (t (142) =

3.279, p * .001) and IQ (t (142) = 2.181, p * .05) and the predictors had partial

correlations of, .440, .264 and .179, respectively. The regression equation in

standardized form for the stepwise regression analysis was Z reading = .408Z ART .248Z

Ravens .168ZIQ. The difference between the first standardized regression equation was

the stepwise regression only includes the variables that significantly contributed to the

prediction. Therefore, working memory and GPA were excluded in the stepwise regression

because they were not good predictors of reading ability. It was also shown that the

stepwise regression was a better type of regression because it was able to significantly

predict predictors (F (2, 140) = 2.278, ns).

For the curve estimates the regression coefficient was significant for the linear

component (t (1,146) = 6.150, p * .00001) therefore there was a positive linear

relationship between reading ability and exposure to print. The regression coefficients

were not significant for the quadratic component (t (1,146) = -.583, ns) or the cubic