Linear Regression results

Hello,

I have a little question. I ran a linear regression model. I got strange results. In the ANOVA table, the F test is not significant. As far as I know, that means that ALL beta's are 0. But, when looking at the independent variables, 1 was significant, meaning that it ain't 0...how can that be possible ?

Here is the R output. SPSS did nearly the same thing...

Call:

lm(formula = Y ~ X + size + v7)

Residuals:

Min 1Q Median 3Q Max

-3.78476 -1.42308 0.07127 1.47043 4.78395

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 1.672734 1.528998 1.094 0.2786

**X 0.419851 0.191985 2.187 0.0329 ***

size -0.001394 0.002407 -0.579 0.5649

v7 0.014232 0.018994 0.749 0.4568

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.108 on 56 degrees of freedom

(104 observations deleted due to missingness)

Multiple R-squared: 0.08521, Adjusted R-squared: 0.03621

**F-statistic: 1.739 on 3 and 56 DF, p-value: 0.1695**