Part A

The director of marketing at Duesoldi wants to study monthly sales of their products, in order to understand how much they depend on the per capita income. He would like to take this into consideration in deciding about expanding the business to other states.

To investigate the relationship between sales and income, the director of marketing at Duesoldi selects at random 10 US states in which their products are sold, and for each of them notes:

• sales, the quantity of products sold last month (in thousands);
• income, the per capita income in the state (in thousands of $).

Below you can find the R output (with some part removed) for a simple regression model of sales on income.

> summary(duesoldi) income sales Min. :23.94 Min. :40.62 1st Qu.:25.86 1st Qu.:43.77 Median :27.41 Median :46.05 Mean :27.72 Mean :46.21 3rd Qu.:29.27 3rd Qu.:46.76 Max. :33.10 Max. :57.14 > cor(income,sales)[1] 0.8074761> reg_duesoldi=lm(sales~income)> summary(reg_duesoldi)Call: lm(formula = sales ~ income)Residuals: Min 1Q Median 3Q Max -4.6047 -1.4825 0.0333 1.7933 3.9455 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 10.2301 9.3355 1.096 0.30504 income 1.2980 0.3353 3.872 0.00473 **---Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Residual standard error: ???? on ???? degrees of freedomMultiple R-squared: ????, Adjusted R-squared: ???? F-statistic: 14.99 on ???? and ???? DF, p-value: 0.00473> reg_red=lm(sales~1)> anova(reg_red,reg_duesoldi)Analysis of Variance TableModel 1: sales ~ 1Model 2: sales ~ income Res.Df RSS Df Sum of Sq F Pr(>F) 1 ???? 185.766 2 ???? 64.643 ???? 121.12 14.99 0.00473 **---Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual Q-Q plot O O O N - O O O O Residuals Sample Quantiles O O O O O O O 42 44 46 48 50 52 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Fitted values Theoretical Quantiles