Find a basis for the subspace V of R3 splmned by S~ ! [i]. m [=;]. m [:]) and write each of the following vectors in lenns of the basis vectors: ) m

MAT 221 – Chapter 2 Looking at Data - Relationships 2.1 & 2.2: Relationships & Scatterplots Scatterplot- one axis is used to represent each of the variables and the data are plotted as points on the graph Three Aspects of a Relationship: 1. Direction- positive or negative a. Positive: greater values of one variable tend to occur w/ greater values of other values (ex. House size and price) b. Negative: greater values of one variable tend to occur w/ smaller values of other variable (ex. Weight of cars and fuel efficiency) 2. Form – linear, curved, clusters, no pattern 3. Strength – how closely the points fit the form No relationship- the variables are independent Explanatory (independent) variable – the one that controls the other variable [x-axis] Response (dependent) variable – the one that moves based on the other variable [y-axis] Outlier- anything that doesn’t follow the trend 2.3 Correlation Correlation (coefficient) r – a numerical measure of the direction and strength of the relationship between 2 quantitative variables Properties: - Value r ranges from -1 to 1 - Gives the direction of the relationship - Closer to 1 or -1 is a strong relationship - Closer to 0 is a weak relationship - Very sensitive to outliers How to calculate: - For each case in the sample we have a pair of values (x,y) - Suppose there are n cases (x1,y1), (x2,y2),