- Statistics assignment
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Statistics assignment

Part C

Table of Contents

Question 1) Statistical inference topic 7. 3

Question 2) Simple linear regression model topic 8. 3

a). 3

b). 4

Question 3) multiple linear regression model topic 9. 6

a). 8

b). 8

Reference. 9

# Question 1)Statistical inference topic 7

For the two variables Dom Time and Non time there are 125 values. Now the average value of Dom time and Non time are 0.43 and 0.45 respectively. Since average value of Non Time is greater than the average value of Dom Time, it can be concluded that reaction time is not quicker using the dominating hand.

# Question 2) Simple linear regression model topic 8

In this problem we have to find the relationship between age and height, using simple linear regression model.

## a)

The scatter plot of these two variables is given by-

This scatter plot indicates that age and height are related, and sign of this relationship is positive.

## b)

The following output is obtained from SPSS

Descriptive Statistics |
|||

Mean | Std. Deviation | N | |

height | 161.8080 | 13.26267 | 125 |

age | 13.6880 | 1.85096 | 125 |

Table: 1

Correlations |
|||

height | age | ||

Pearson Correlation | height | 1.000 | .603 |

age | .603 | 1.000 | |

Sig. (1-tailed) | height | . | .000 |

age | .000 | . | |

N | height | 125 | 125 |

age | 125 | 125 |

Table: 2

Model Summary |
|||||||||

Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | Change Statistics | ||||

R Square Change | F Change | df1 | df2 | Sig. F Change | |||||

1 | .603^{a} |
.363 | .358 | 10.62655 | .363 | 70.152 | 1 | 123 | .000 |

a. Predictors: (Constant), age Table: 3 | |||||||||

b. Dependent Variable: height |

Coefficients |
||||||

Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||

B | Std. Error | Beta | ||||

1 | (Constant) | 102.700 | 7.121 | 14.423 | .000 | |

age | 4.318 | .516 | .603 | 8.376 | .000 | |

a. Dependent Variable: height Table: 4 |

From table 1 it is cleared that correlation between age and height .603, and significance value (p value) of this correlation is .000. Since p value of this correlation is less than 0.05, it can be said that correlation between age and height are statistically significant. So age and height are positively correlated. Value of coefficient of determination (R square) is 0.363; this value is obtained from table2. . R square is a measure, which is used to measure how close the actual data to the fitted regression line. Simply R square is the percentage or proportion of the total variation which is explained by this multiple regression model. 0.363 is not so much high. So it can be concluded that we cannot get good fit using this model. Here the regression equation(least square regression line) is Yt= 102.700 + 4.318Xt, here Y is the dependant variable, i.e. height and X is the independent variable i.e. age, and t represents the total number of variable, for this problem t is 125. In regression analysis it is very important to study the significance of the estimated coefficients. In regression model the confidents indicates the average change in dependent variable with respect to per unit change in independent variable. To test this significance of coefficient consider the following hypothesis –

H0: there is no relationship between age and height against the alternative H1: there is relationship between age and height (DiMaggio, 2013).

By regression analysis we can get the significance value of coefficients. If this significance value is less than 0.05, then we can reject the null hypothesis at 0.05 level of significance.

From the table 4 it can be said that significance value (p value) of the coefficient of independent variable (age) is .000. So it can be said that height depends on age(Thomson, and Emery, 2014).

# Question 3) multiple linear regression model topic 9

The following output is obtained from SPSS

Correlations |
||||

height | age | sex | ||

Pearson Correlation | height | 1.000 | .603 | -.227 |

age | .603 | 1.000 | .010 | |

sex | -.227 | .010 | 1.000 | |

Sig. (1-tailed) | height | . | .000 | .005 |

age | .000 | . | .458 | |

sex | .005 | .458 | . | |

N | height | 125 | 125 | 125 |

age | 125 | 125 | 125 | |

sex | 125 | 125 | 125 |

Table: 1

Model Summary^{b} |
|||||||||

Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | Change Statistics | ||||

R Square Change | F Change | df1 | df2 | Sig. F Change | |||||

1 | .646^{a} |
.417 | .408 | 10.20634 | .417 | 43.692 | 2 | 122 | .000 |

a. Predictors: (Constant), sex, age Table: 2 | |||||||||

b. Dependent Variable: height |

Coefficients^{a} |
||||||

Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||

B | Std. Error | Beta | ||||

1 | (Constant) | 111.506 | 7.322 | 15.229 | .000 | |

age | 4.334 | .495 | .605 | 8.752 | .000 | |

sex | -6.164 | 1.831 | -.233 | -3.367 | .001 | |

Table: 3 |

## a)

From table 1 it can be said that correlation between sex and height -0.227, and significance value (p value) of this correlation is .005. Since significance value of this correlation is less than 0.05, it can be said that correlation between sex and height are statistically significant. So age and height are negatively correlated for this data set. Value of coefficient of determination (R square) is 0.417; this value is obtained from table2. . R square is a measure, which is used to measure how close the actual data to the fitted regression line. Simply R square is the percentage or proportion of the total variation which is explained by this multiple regression model (Menke, 2012). Since 0.417 is not so much high, it can be concluded that we cannot get good fit using this model. Here the regression equation (least square regression line) is Yt= 111.506 + 4.334Xt – 6.164 X’t, here Y is the dependant variable ( height) and X is the first independent variable(age), and X’t is the second independent variable (sex), t represents the total number of variable, for this problem t is 125. In regression analysis it is very important to study the significance of the estimated coefficients. In regression model the confidents indicates the average change in dependent variable with respect to per unit change in independent variable. To test this significance of coefficient consider the following hypothesis –

H0: there is no relationship between sex and height against the alternative H1: there is relationship between sex and height(endat, and Piersol, 2011).

By regression analysis we can get the significance value of coefficients. If this significance value is less than 0.05, then we can reject the null hypothesis at 0.05 level of significance(Gelman, *et al*, 2014).

Table 3 indicates that significance value of the coefficient of sex is .001. Since 0 .001 is less than 0.05, it can be concluded that height depends on sex(Agresti, 2013).

## b)

R square value of the first regression model (question 2) is 0.363, and R square value of the second regression model is .417. It is known that R square is the measure of goodness of fit. Higher the value of R square, better the fit. So, sex makes a significant contribution to the regression model(DiMaggio, 2013).

# Reference

Hair, J. F. (2010). Multivariate data analysis.

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2014). *Bayesian data analysis* (Vol. 2). Chapman

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2014). *Bayesian data analysis* (Vol. 2). C

Agresti, A. (2013). *Categorical data analysis*. John Wiley & Sons.

endat, J. S., and Piersol, A. G. (2011). *Random data: analysis and measurement procedures* (Vol. 729). John Wiley & Sons.

Menke, W. (2012). *Geophysical data analysis: discrete inverse theory*. Academic press.

Thomson, R. E., & Emery, W. J. (2014). *Data analysis methods in physical oceanography*. Newnes.

DiMaggio, C. (2013). *Introduction* (pp. 1-5). Springer New York.