Question

The data below show sales of daily ice cream in thousands of dollars and the temperature
in Fahrenheit for 21 consecutive days in an ice cream shop. Assuming there is a linear
relationship between the two, find the regression coefficients using the formulae for αhat
and βhat (not the Excel regression tool).

                        Daily High                  Sales Per Store

                        Temperature                (Thousands of

Day                 (Degrees F)                 Dollars)                    

1                      63                                1.52

2                      70                                1.68

3                      73                                1.80

4                      75                                2.05

5                      80                                2.36

6                      82                                2.25

7                      85                                2.68

8                      88                                2.90

9                      90                                3.14

10                    91                                3.06

11                    92                                3.24

12                    75                                1.92

13                    98                                3.40

14                    100                              3.28

15                    92                                3.17

16                    87                                2.83

17                    84                                2.58

18                    88                                2.86

19                    80                                2.26

20                    82                                2.14

21                    76                                1.98  

βhat=

αhat=

?=????−?????2−??2and  ?=?−??β ̂=(∑▒〖x_i y_i-Nx ̄y ̄ 〗)/ (∑▒〖x_i^2-Nx ̄^2 〗) and α ̂=y -β ̂x

Answer 1