Question

1) The highway mileage (mpg) for a sample of 8 different models of a car company can be found below.

17, 21, 23, 26, 36, 29, 33, 36

Find the 5-number summary, check for any outliers using fences, and create a boxplot.

Use the space below to type your answers AND/OR to upload a picture of your work for all the questions in this problem.

2)

A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).

The results of the regression were:

ˆyy^=a+bx
a=-1.148
b=0.065

(a) Write the equation of the Least Squares Regression line of the form

y^= + x

(b) Which is a possible value for the correlation coefficient, rr?

• 0.807
• 1.247
• -0.807
• -1.247

(c) If a country increases its life expectancy, the happiness index will

• increase
• decrease

(d) If the life expectancy is increased by 4.5 years in a certain country, how much will the happiness index change? Round to two decimal places.



(e) Use the regression line to predict the happiness index of a country with a life expectancy of 67 years. Round to two decimal places.



Use the space below to type your answer AND/OR to upload a picture of your work for all the questions in this problem.

Answer 1

Que.1

To solve this question we use R software.

R codes and output:

> x=c(17, 21, 23, 26, 36, 29, 33, 36)

> summary(x)

   Min. 1st Qu. Median    Mean 3rd Qu.    Max.

17.00   22.50   27.50   27.62   33.75   36.00

> boxplot(x)

20 25 30 35

There is no outlier present in the data.

Que.2

a.

The Least Squares Regression line is

y = -1.148 + 0.065 x

b.

Here slope coefficient is positive, hence correlation is also positive. And we know that correlation always lies between -1 to +1

hence possible value of correlation coefficient r = 0.807

c.

Increases.

Because correlation coefficient is positive.

d.

Happiness index =  0.065 * 4.5 = 0.29

Happiness index will increased by 0.29

e.

Happiness index is computed as follows:

y = -1.148 + 0.065 x

y = -1.148 + 0.065 (67)

y = 3.21