Regression Code (questions below) fit summary(fit) Call: lm(formula = Price ~ Carat) Residuals: Min1QMedian3QMax -85.159 -21.448-0.86918.97279.370 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept)-259.6317.32-14.99 <2e-16

Regression Code (questions below)

fit<-lm(Price~Carat)

> summary(fit)

Call:

lm(formula = Price ~ Carat)

Residuals:

Min1QMedian3QMax

-85.159 -21.448-0.86918.97279.370

Coefficients:

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

(Intercept)-259.6317.32-14.99<2e-16 ***

Carat3721.0281.7945.50<2e-16 ***

---

Signif. codes:0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 31.84 on 46 degrees of freedom

Multiple R-squared:0.9783,Adjusted R-squared:0.9778

F-statistic:2070 on 1 and 46 DF,p-value: < 2.2e-16

Regression

Write down the regression line equation when using Carat as the independent variable and Price as the dependent variable.

Write down the R2 value. What does this mean in terms of the data?

Test the hypothesis that 0 (show your hypotheses & conclude/interpret).

Using the regression line, what is the predicted price of a diamond with a carat size of 0.3?

What would be the predicted price of a 0.7 carat diamond? Do you trust this estimate?

Correlation Code (questions below)

cor.test(Carat,Price,alternative="two.sided")

Pearson's product-moment correlation

data:Carat and Price

t = 45.497, df = 46, p-value < 2.2e-16

alternative hypothesis: true correlation is not equal to 0

95 percent confidence interval:

0.9804794 0.9938925

sample estimates:

cor 0.9890707

What is the correlation of your two variables?

Test that 0 (show hypotheses/conclude/interpret).

Based only on your correlation, would you say that a higher carat causes higher diamond prices? Thank you