4. 10 points) In a sample of adults, the number of years of schooling completed was...

> y=c(15,6,9,16,12,18,12,14,14)

> x=c(13,9,12,16,12,16,13,13,18)

> reg=lm(y~x)

> reg

Call:

lm(formula = y ~ x)

Coefficients:

(Intercept)            x

     -1.676        1.074

#Mothers High school year=-1.167+1.074*Respondent’s highest school year completed

Hence there is linear relationship between two variable.

> cor(y,x)

[1] 0.7929672

Correlation coefficient is 0.79% hence there is higher positive correlation.

> summary(reg)

Call:

lm(formula = y ~ x)

Residuals:

    Min      1Q Median      3Q     Max

-3.6641 -1.9943 0.4847 1.7080 2.7080

Coefficients:

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

(Intercept)   -1.676      4.303 -0.389   0.7086

x              1.074      0.312   3.443   0.0108 *

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

Residual standard error: 2.381 on 7 degrees of freedom

Multiple R-squared: 0.6288,   Adjusted R-squared: 0.5758

F-statistic: 11.86 on 1 and 7 DF, p-value: 0.01079

P_value =0.0108 < 0.05 hence we can say that our regression coefficient is significantly different from zero. therefore Respondent’s highest school year completed is significant variable.

> confint(reg, "x" ,level=0.95)

      2.5 %   97.5 %

x 0.3366239 1.812231

Confidence  interval is [0.3366239 , 1.812231]