Bivariate Correlation and Regression

When observing a Correlation, the researchers are determining or measuring whether a

relationship exists and explaining the strength of the relationship (Frankfort-Nachmias &

Leon-Guerrero, 2018). In other words, a Correlation tells us the "extent to which

variables are related" (Wagner, 2020). Correlation ranges from -1.0 to +1.0; never

above or below this range.If it is outside of this range, there is an error.

Also being shown will be a regression table. Regression is used to predict how one or more independent variables can affect the dependent variable (Frankfort-Nachmias & Leon-Guerrero, 2018. A Bivariate Regression analyzes how changes in one independent variable can affect the dependent variable being studied.

Research Question: Is there a linear relationship between a math teachers' self-efficacy and the number of years the teacher has taught high school math?

Both variables are continuous, and there is an assumption that an educator's belief in their capabilities gets better with more experience; therefore, there might be a linear relationship. Both assumptions are met (Frankfort-Nachmias, et al., 2020).

A standard linear regression was calculated to create predictions about math teachers' self-efficacy based on how many years the teacher has been teaching high school math. As shown in Table 1, a significant regression equation was found (F (1,3668) = 28.133, p < .001), with R2 = .01 (Table 2). The regression equation is: math teacher's self-efficacy = .003 + .010 * years math teacher has taught high school math (Table 3). Math teacher's self-efficacy increased by .010 for each year a math teacher has taught high school math. About 1% of the math teacher's self-efficacy is explained by the variable years math teacher has taught high school math

.

Table 1. ANOVAa
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	25.174	1	25.174	28.133	<.001b
Residual	3282.200	3668	.895
Total	3307.374	3669
a. Dependent Variable: T1 Scale of math teacher's self-efficacy

Table 2

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.087a	.008	.007	.94595
a. Predictors: (Constant), Years math teacher has taught high school math

Table 3. Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
B	Std. Error	Beta
1	(Constant)	.003	.024		.126	.900
Years math teacher has taught high school math	.010	.002	.087	5.304	<.001
a. Dependent Variable: T1 Scale of math teacher's self-efficacy

Implications for Social Change

In order to improve planning of math courses offered and placement of teachers to teach those courses, it is essential to gain understanding about a math teacher's confidence in their abilities and if their confidence is affected by their years of experience teaching math at the high school level. Further research may involve studies pertaining to how to improve teacher training by raising teacher self-efficacy, therefore increasing teacher retention.

Is this correct? Does it make sense?