1877 words - 8 pages

1. A scatter-plot is a graph made by plotting ordered pairs in a coordinate plane to show the correlation between two sets of data. It helps to show us the trends between the two variables for example whether there is a positive correlation, a negative correlation or no correlation at all.

This graph shows the relationship between hours and age. We can see from the regression line that there is a negative correlation between the two variables. The correlation table for gives a correlation coefficient of -0.4222. This shows quite a strong negative association. This means that the older you are the fewer hours you will work.

| HOURS |

AGE | -0.422170403728502 |

Here we have a graph ...view middle of the document...

Error | t-Statistic | Prob. |

| | | | |

| | | | |

C | 18.22848 | 1.431566 | 12.73324 | 0.0000 |

WAGE | 2.293989 | 0.181412 | 12.64520 | 0.0000 |

| | | | |

| | | | |

R-squared | 0.349204 | Mean dependent var | 32.55000 |

Adjusted R-squared | 0.347020 | S.D. dependent var | 18.76792 |

S.E. of regression | 15.16582 | Akaike info criterion | 8.282610 |

Sum squared resid | 68540.67 | Schwarz criterion | 8.307302 |

Log likelihood | -1240.392 | Hannan-Quinn criter. | 8.292492 |

F-statistic | 159.9010 | Durbin-Watson stat | 1.971576 |

Prob(F-statistic) | 0.000000 | | | |

| | | | |

| | | | |

Regression analysis is used to analyse how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. It also helps to explain the impact of changes in an independent variable on the dependent variable.

The linear relationship between hourly wage and hours worked can be expressed using the equation, which we estimate through the Ordinary Least Squared Method (OLS):

Hours worked = 18.23 + 2.29 Wage

β1 represents the slope (or the change in hours worked per unit change in wage rate)

The coefficient of determination (R²) is the portion of the total variation in the hours worked (the dependant variable) that is explained by variation in the wage rate (the independent variable). This basically is trying to explain the effect that wage has on the number of hours worked. From the table above R²= 0.3492 (which we can round up to 35%) which shows that about 35% of the variation in hours worked is due to the variation in the wage rate.

The standard error of regression (SER) measures the amount of variability in the points around the regression line. It is the standard deviation of the data points as they are distributed around the regression line. The standard error of the estimate can be used to develop confidence intervals around a prediction. A smaller S.E of regression represents a more accurate estimation. With the data we have in this case the S.E of regression is 15.27 and if we take into consideration the sample size of 300 it can be said that it is reasonably accurate.

Null and alternative hypotheses

H0: β1 = 0 (no linear relationship)

H1: β1 0 (linear relationship does exist)

To calculate the t- statistic we use the equation shown below

t = (2.294 – 0) / 0.1814 = 12.65

tn-2,α=t298,0.05=1.645

We reject the null hypothesis as the t-statistic is larger than the critical value (12.65>1.645) and we favour the alternative hypothesis. Hence we conclude that there is strong evidence that there is a linear correlation between the two variables, an increase in hours worked leads to an increase in wage.

The F-statistic test confirms the result of the t- test. Also due to the fact that the F-statistic (159.9) > F1,n-2,α, we can reject the null hypothesis of no...

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