Question

A team of researchers in Economics are investigating the relation between annual income and weekly savings of families. It is supposed that the higher the income, the more will be the predisposition of a family to save money, with savings and income linked through a linear relationship. The team collected data for a sample of 157 families, recording the overall annual income (in 1000 of euros) and the average weekly savings (in euro) over a period of one year. The data are shown in the scatterplot below.

The following summary quantities are calculated from the data. The following summary quantities are calculated from the data. ∑ i xi = 7290 ∑ i yi = 21109 ∑ i x 2 i = 435086 ∑ i y 2 i = 3876015 ∑ i xiyi = 1208801.

1. Estimate the regression line between savings and income and provide an interpretation of the parameters.

2. Calculate the coefficient of determination.

3. Compute a 95% confidence interval for the slope of the regression model.

4. Without doing any calculations, perform a model utility test taking α = 0.05. Discuss the steps and the result.

5. The researchers theorized that each 1000 euro increase in annual income should correspond on average to more than 2 euro increase in the mean weekly savings of a family. Do the data support this theory? (Use α = 0.05)

Answer 1

2.37 24-54 SST

SSて 2.39土 2.602,.2.223