Degrees: Pharmacy, Biotechnology

Date: November 28, 2016

## Question 1

The table below gives the distribution of points obtained by students in the MIR exam last year.

- Compute the interquartile range and explain your result. Are there outliers in the sample?
- The minimum number of points to pass the exam is 150; what percentage of students passed the exam?
- Study the representativity of the mean.
- According to the values of skewness and kurtosis, can we assume that the sample has been taken from a normally distributed population?
- Compute the standarized points of a student that got 150 points in the MIR.

## Question 2

The table show the data of the GDP (Gross Domestic Product) per capita (thousands of euros) and infant mortality (children per thousand) from 1993 till 2000.

Year | GDP | Mortality |
---|---|---|

1993 | 17 | 6.0 |

1994 | 17 | 5.6 |

1995 | 18 | 5.2 |

1996 | 18 | 4.9 |

1997 | 19 | 4.6 |

1998 | 20 | 4.3 |

1999 | 21 | 4.1 |

2000 | 22 | 4.0 |

- Estimate the value of the GDP for an infant mortality of 3.8 children per thousand using the linear regression model.
- Which regression model explains better the GDP as a function of the infant mortality, a linear model or an exponential one?
- If we assume that the GPD per capita in year 2001 was 23 thousand €, what will be the expected infant mortality, according to the exponential regression model?
- Consider the linear models of GDP on infant mortality, and infant mortality on GDP; which of the two is more reliable?

Use the following sums for the computations ($X$=GDP and $Y$=Infant mortality): $\sum x_i=152$, $\sum \log(x_i)=23.5229$, $\sum y_j=38.7$, $\sum \log(y_j)=12.5344$, $\sum x_i^2=2912$, $\sum \log(x_i)^2=69.2305$, $\sum y_j^2=190.87$, $\sum \log(y_j)^2=19.7912$, $\sum x_iy_j=726.5$, $\sum x_i\log(y_j)=236.3256$, $\sum \log(x_i)y_j=113.3308$, $\sum \log(x_i)\log(y_j)=36.76$.

## Question 3

Consider two variables $X$ and $Y$. Assume that the regression lines of the linear models intersect at the point $(2,3)$, and that, according to the appropriate linear model, the expected value of $Y$ for $x=3$ is $y=1$. How much will $Y$ change, according to the linear model, when $X$ increases by one unit?

If the coefficient of linear correlation is $-0.8$, how much will $X$ change, according to the linear model, when $Y$ increases by one unit?