Foundations of Statistics - Tutorial Week 9 relationship between two Metric Variables Learning Objectives V Be able to produce and interpret a scatterplot and Pearson's r in SPSS v Be able to interpret the 95% confidence interval for a correlation V Understand that a correlation does not necessarily mean a causal relationship Exercises: Produce the scatterplots, and where appropriate, the correlation analysis and 95% Confidence Interval information using the following data files: Snakes.sav Is there evidence of a relationship between the weight of snakes and their length? How did you make this decision? Quote relevant statistics to support the decision made. Graph -> Scatter/Dot -> Simple Scatter (Scatterplot) Analyze -> Correlation -> Bivariate -> Confidence interval
.1380 R2 Linear = 0.678 .1360 .1340 y =- 0.01+0.22*x Weight of Snake [kg] . O .1320 O .1300 0 .1280 .6400 .6450 .6500 .6550 .6600 .6650 .6700 Length of Snake [m] Correlations Length of Snake [m] 1 Length of Snake [m] Pearson Correlation Sig. (2-tailed) N 15 Weight of Snake [kg] Pearson Correlation .824 ** Sig. (2-tailed) <. 001 N 15 **. Correlation is significant at the 0.01 level (2-tailed). Weight of Snake [kg] .824* <. 001 15 1 15 Length of Snake [m] - Weight of Snake [kg] Confidence Intervals 95% Confidence Intervals (2-tailed)ª Pearson Correlation .824 Sig. (2- tailed) <. 001 Lower .539 Upper .940 a. Estimation is based on Fisher's r-to-z transformation.
Sales_&_Staff.sav For the company is there evidence of a relationship between the sales revenue [$m] and number of sales staff in the offices? How did you make this decision? Quote relevant statistics to support the decision made. R2 Linear = 0.745 70 60 Sales [$m] 50 y =- 0.77+2.07*x 40 O . O 30 15.0 17.5 20.0 22.5 25.0 27.5 Number of Sales Staff Correlations Sales [$m] Number of Sales Staff Pearson Correlation 1 Sig. (2-tailed) N Pearson Correlation .863* Sig. (2-tailed) .001 N 10 Sales [$m] 10 10 **. Correlation is significant at the 0.01 level (2-tailed). Number of Sales Staff .863 .001 1 10