Example: Ice Cream Sales										
										
The local ice cream shop keeps track of how much ice cream they sell versus the temperature of that day for the last 12 days:										
Formulate a null hypothesis and verify it by Pearsons and Spearman coefficients										
										
				Ho: there is no correlation						
				H1: There is correlation						
										
	Temperature (°C)	Ice Cream Sales ($)		rank t	rank sales	d	d2		Spearman's law	
	14.2	215		11	11	0	0			
	16.4	325		9	10	-1	1			
	11.9	185		12	12	0	0			
	15.2	332		10	9	1	1			
	18.5	406		6	8	-2	4			
	22.1	522		4	3	1	1			
	19.4	412		5	6	-1	1			
	25.1	614		1	1	0	0			
	23.4	544		2	2	0	0		0.587	crit
	18.1	421		7	5	2	4			
	22.6	445		3	4	-1	1		0.951048951	
	17.2	408		8	7	1	1			
							14			
average	18.7	402.4								
										
	-4.5	-187.4	838.7							
	-2.3	-77.4	176.1							
	-6.8	217.4166667	-1473.0		Pearson's law					
	-3.5	-70.4	244.6							
	-0.2	3.6	-0.6							
	3.4	119.6	409.6							
	0.7	9.6	6.9							
	6.4	211.6	1354.1							
	4.7	141.6	669.0							
	-0.6	18.6	-10.7							
	3.9	42.6	167.1							
	2.3	5.6	13.0							
										
	179.9	174756.7425	2394.994167		0.427151283					
										
					0.576	crit				
										
						H0= is rejected. 				
##### Sheet/List 2 #####
age (yrs)	price/1000 Kč		Here is a pricelist of used 10 cars Skoda Felicia Combi
3	167		
4	165		1. pressume normal distribution of the data
5	139		2. construct a simple regression model  how the price depends on the age
6	149		3. evaluate quality of the model
7	119		4. estimate a price of a ten-year-old Felicia Combi
7	129		
8	89		
8	115		
9	76		
9	89		
##### Sheet/List 3 #####
"A new kind of insulin was developed. Its effect was tested as a drop of sugar level in blood  2 hours after the injection application. 
8 Randomly selected patients were dozed with different insulin amounts. Results are in the table: "	Prove a strong correlation and plot a graph of regression residuals!													
														
														
insuline amount (ug)	150	200	250	300	350	400	450	500						
sugar level drop (%)	8	12	30	20	55	58	44	65						
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
														
##### Sheet/List 4 #####
concentration	signal
1	0.195
2	0.425
3	0.565
4	0.851
5	1.142
6	1.198
7	1.530
	
HOW TO FORCE Const a=0