Simple linear regression

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Simple linear regression

A regression analysis between only two variables, one dependent and the other explanatory.
Copyright © 2012, Campbell R. Harvey. All Rights Reserved.

Simple Linear Regression

In statistics, the analysis of variables that are dependent on only one other variable. Regression analysis uses regression equations, which shows the value of a dependent variable as a function of an independent variable. For example, a simple regression equation could take the form:

y = a + bx

where y is the dependent variable and x is the independent variable. In this case, the slope is equal to b and a is the intercept. When plotted on a graph, y is determined by the value of x. Regression equations are charted as a line and are important in calculating economic data and stock prices. See also: Multiple regression.
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References in periodicals archive ?
For hypothesis 3 testing a series of simple linear regressions that were done for testing the hypotheses 1 and 2 were repeated, but separately for the group of small, medium and large-sized car servicing companies.
First of all we made a series of simple linear regressions, with overall customer satisfaction as an independent variable and with several financial ratios for each year (2009, 2010 and 2011) as dependent variables.
For testing hypothesis 3, stating: "There are statistically significant differences regarding customer satisfaction influence on chosen financial ratios between the car servicing companies of various sizes", we performed separate simple linear regressions for groups of small, medium and large-sized car servicing companies.
4: Results of simple linear regressions for small-sized car servicing companies Financial ratio SMALL-SIZED CAR SERVICING COMPANIES (N=7) Dependent variable Standardized beta adjusted [R.sup.2] OPM-Service09 -0.806 0.579 OPM-Service10 -0.894 * 0.759 * OPM-Service11 -0.941 * 0.863 * OPM-Service09-11 -0.899 * 0.770 * PTPM-Service09 -0.756 0.486 PTPM-Service10 -0.772 0.515 PTPM-Service11 -0.748 0.472 PTPM-Service09-11 -0.790 0.549 OPM = operating profit margin PTPM = pre-tax profit margin * Statistically significant at p < 0.01.
Based on simple linear regressions, the results showed that almost all of the variables considered were significantly correlated with species richness (Table 2).
In this study, the relationship between the explanatory variables and species richness was calculated for each individual variable using simple linear regression then overall using stepwise multiple linear regression analyses.
If the correlation between these two variables was positive in simple linear regression analysis, Rapoport's elevational rule would be supported.
On the contrary, there was a negative and insignificant (P > 0.01) correlation between these two variables in simple linear regression model and the correlation coefficient was very low ([R.sup.2] = 0.003, 0.001, 0.004, 0.081 for overall plants, seed plants, bryophytes, and ferns, resp.) (Figure 5).
Table 3 Simple Linear Regressions of Age, Weight, and HOURSPST on BUN, DIFFBUN, Creatinine, and DIFFCRTN
Data analysis was performed using independent sample t-tests, simple linear regression, ANOVA, and multiple comparisons.
Variable Gender N Mean SD T P BUN Male 175 31.23 mg/dl 10.17 mg/dl 2.49 .01 Female 108 28.49 mg/dl 6.61 mg/dl 2.75 .00 DIFFBUN Male 166 -8.65 mg/dl 12.98 mg/dl -.17 .86 Female 102 -8.39 mg/dl 10.60 mg/dl -.18 .86 Creatinine Male 175 2.33 mg/dl .69 mg/dl 3.34 .00 Female 108 2.06 mg/dl .64 mg/dl 3.40 .00 DIFFCRTN Male 166 -.63 mg/dl .68 mg/dl -.19 .85 Female 102 -.62 mg/dl .52 mg/dl -.21 .84 HOURSPST Male 175 45.70 hrs 31.04 hrs -.64 .53 Female 108 48.39 hrs 39.84 hrs -.60 .55 Simple linear regression showed that BUN was predicted by HOURSPST (t = -5.10, p = .00), and both BUN (t = -2.07, p =.
(We begin to see why it took Borrel ten years to collect her data and conduct her analyses.) To the extent that we trust simple linear regressions for short periods as representations of cause and effect in labor-management-state interactions, Borrel's statistical results give some comfort to conventional expectations that unemployment dampens strike activity, while price increases, worker mobilization, and left political power promote it.