Question

Is there a relationship between the dollars spent each week on recreation and the number of members of the family? Do larger families spend more on recreation? Ten Chicago families shared the following information:

Family Size               3         6        5        6        6        3        4         4         5        3

Amount Spent          99        104     151     129     142     111     74        91        119     91

h. Predict the recreational spending for a family of size 5.

i. If there are families of that size in the data set, what are the residuals for those observations?

j. Test the explanatory power of the model at a 5% level of significance.

k. Test if there is a positive relationship between family size and recreational spending. Use alpha = 0.01.

l. What is the excel command used to produce the p-value associated with the test in part k?

Answer 1

Family_Size<-c(3,6,5,6,6,3,4,4,5,3)
Amount_Spent<-c(99,104,151,129,142,111,74,91,119,91)
mod<-lm(Amount_Spent~Family_Size)
mod
summary(mod)
summary.aov(mod)

h. Predict the recreational spending for a family of size 5.

i. If there are families of that size in the data set, what are the residuals for those observations?\

Residuals are 34.2620690 and 2.2620690 for 3rd and 9th observations

j. Test the explanatory power of the model at a 5% level of significance.

The R-squared is called the coefficient of determination tells us how well the model explains the variation in the model is =0.3471 or 34.71% variation in the y variable is explained by the model.

k. Test if there is a positive relationship between family size and recreational spending. Use alpha = 0.01.

For Alpha =0.01 we cannot reject the null hypothesis and thus we can say there is no significant relationship between the two variables.