Question

Intelligence Test Score 110 105 95 130 141 102 101 90 87 110

Performance Ratings 5.1 4.2 3.1 6.8 6.7 3.7 3.2 3.0 1.8 4.4

1) Test if there is a significant linear correlation between intelligence test scores and performance ratings. Use. Step1) Identify the null and alternative hypotheses symbolically. H0: H1: Step 2) a) Find the p-value and make a decision to reject or not reject the null hypothesis. (SHOW WORK) b) Is there a linear relationship between intelligence test scores and performance ratings?

2) Find the equation of the regression line for the data.

3) Using the equation of the regression line to predict the rating for an intelligence score of 103.

Answer 1

Here I attach R code

x=c(110, 105 ,95, 130 ,141 ,102, 101, 90 ,87, 110)
y=c(5.1, 4.2, 3.1, 6.8 ,6.7, 3.7 ,3.2 ,3.0, 1.8, 4.4)
cor.test(x,y)
m=lm(y~x)
summary(m)

$H_o:\rho=0 \\ H_1:\rho\neq0$

Pearson's product-moment correlation data: x and y t = 10.118, df = 8, p-value = 7.776e-06 alternative hypothesis: true correlation is not equal to o 95 percent confidence interval: 0. 8471379 0.9914870 sample estimates: 0.9630776

Here since the p value is < 0.05 we reject the null hypothesis that there is no correlation

The correlation is 0.9630776

Coefficients: Estimate std. Error t value Pr(ItI) (Intercept) -5.608612 0.980356-5.721 0.000444 0.091584 0.009052 10.118 7.78e-06

2)equation of the regression line for the data.

Performance Ratings = -5.608612+0.091584*Intelligence Test Score

3) 5.608612+(0.091584*103)= 15.04176